UK opposition parties have agreed not to back Boris Johnson's demand for a general election before the EU summit in mid-October.
Labour, the Lib Dems, the SNP and Plaid Cymru say they will vote against the government or abstain in Monday's vote on whether to hold a snap poll.
But the PM said the parties were making an "extraordinary political mistake".
Meanwhile, a bill designed to prevent a no-deal Brexit has been approved by the House of Lords and will pass into law.
It will force the prime minister to ask the EU for the Brexit deadline to be extended beyond 31 October if no deal is agreed by the UK and Brussels by 19 October.
Mr Johnson wants an election to take place on 15 October, ahead of that date and the EU summit on 17 and 18 October.
He argues that a snap poll will allow the government to "get on" with delivering Brexit by the end of October.
But opposition MPs - who, along with Conservative rebels, have already defeated one attempt by the government to bring in an early election - say Mr Johnson is trying to push through a no-deal exit.
During the past week the prime minister has suffered several defeats over Brexit in Parliament, expelled 21 of his own MPs for rebelling and seen his younger brother, Jo Johnson, resign from government.
In other developments:
Following the meeting of opposition parties on Friday, a Labour Party spokesman said: "Jeremy Corbyn hosted a positive conference call with other opposition party leaders this morning.
"They discussed advancing efforts to prevent a damaging no-deal Brexit and hold a general election once that is secured."
By John Pienaar, BBC deputy political editor
As good weeks go, for Boris Johnson this wasn't one.
Defeated and defeated again in the Commons, choosing to sack more than 20 of his most respected though rebellious colleagues - provoking uproar from Tories who say that was brutally heavy-handed, and now trying to sound conciliatory.
The list of Tory MPs standing down at the next election has continued to grow, and they look like reinforcing Mr Johnson's critics.
And the House of Lords sent legislation to ban no-deal, and maybe force the PM to seek a Brexit extension, to become law.
He won't break his word. Civil servants are clear he can't break the law. Mr Johnson needs a way to force an election, or salvage his plan to deliver Brexit - maybe without getting an EU deal first. In Downing Street there's no sign they've found one.
The options on No 10's table - after another expected defeat on election timing next week - range from quitting office in hope of getting back in, to counting on the EU to deny the UK the Brexit extension the PM doesn't want.
If there's a cunning plan - and many people, in and out of government, don't believe there is - it seems to need more work. And soon.
SNP Westminster leader Ian Blackford said he was "desperate for an election", but it could not happen until an extension to Article 50 - the process by which the UK is leaving the EU - had been secured.
"It's not just about our own party interests; it's about our collective national interests," he said. "So we are prepared to work with others to make sure we get the timing right."
He said they wanted to make sure the UK did not "crash out" in a no-deal Brexit.
Liz Saville Roberts, Plaid Cymru's Westminster leader, said there was an "opportunity to bring down Boris" and "we should take that".
And a Lib Dem spokeswoman said the group was clear that "we are not going to let Boris Johnson cut and run".
"The Liberal Democrat position for a while now is that we won't vote for a general election until we have an extension agreed with the EU. I think the others are coming round to that," she said.
"As a group we will all vote against or abstain on Monday."
But Housing, Communities and Local Government Secretary Robert Jenrick said the public were "sick of watching politicians bicker" about Brexit and it was time for an election.
He said opposition parties should "stop being cowardly, put the matter to the public, and get resolution at last, so the country can move forward with confidence and optimism for the future".
Mr Johnson has promised the UK will leave the EU "do or die" on 31 October, with or without a deal.
But he said on Friday that he would go to Brussels on 17 October and reach a deal.
He added that resigning as prime minister if he did not get one by then was "not a hypothesis" he would be willing to contemplate.
He also said he was "perplexed" by the decision of opposition parties to "run away" from an election.
"All I see is Corbyn and the SNP clubbing together to try and lock us into the EU when it's time to get this thing done," he said.
"It's the most sensational paradox - never in history has the opposition party been given the chance for election and has turned it down."

An internal UK government memo on the consequences of Boris Johnson's Brexit deal renegotiation singles out the removal of the word "adequate" from the UK-EU Political Declaration to describe mechanisms for enforcing common social, environmental, and labour standards after Brexit.
The word "adequate" appears to have been replaced by the word "appropriate".
Extracts of a note written for the government's cross-Whitehall Economic Partnership Steering Group, and seen by the BBC, say the "parties will include "appropriate" (rather than "adequate") mechanisms for dispute settlement" of key "level playing field commitments" in a future trade deal with the European Union.
The consequence of that change, the note says, is that it means that it is now possible to argue it is "inappropriate for the future UK-EU relationship" that disputes about these commitments on employment, environment, tax, state aid and other standards should be subject to binding arbitration.
The memo, first leaked to the Financial Times and marked "Official Sensitive", contains a series of claimed negotiation wins from the Brexit deal renegotiation, weakening the scope and strength of Level Playing Field Commitments (LPF), a crucial element in a future UK-EU trade arrangement.
"The previous Protocol applied wide-ranging LPF measures on a UK-wide bases as a response to UK access to the EU market through the single customs territory.
"UK negotiators successfully resisted the inclusion of all UK-wide LPF rules" says the memo, with the last four words put in bold for emphasis.
"The only level playing field provisions in the revised Protocol are those necessary to support the operation of the Single Electricity Market and state aid measures that affect trade between NI and the EU," it says.
The title of the memo is "Update to EPSG (Economic Partnership Steering Group) on Level Playing Field Negotiations".
This is the first acknowledgement that changing the Level Playing Field commitments agreed by Theresa May was a specific aim of the PM's renegotiation.
In public, the PM focused on changing what he referred to as "the anti-democratic backstop", which had been rejected by the government's parliamentary allies, the Democratic Unionists.
In the end, the PM's new solution, creating a new trade and regulatory border in the Irish Sea, further alienated the DUP. Backbench eurosceptic Conservative MPs have, however, been won over to the deal.
Theresa May's original 2018 deal included a range of specific enforceable common standards for the UK and the EU within the legally binding Withdrawal Treaty.
Some of these standards were related to EU law, others referred to the OECD (Organisation for Economic Cooperation and Development), International Labour Organisation and the Council of Europe.
These were all removed, along with the backstop, and the only reference remaining in the overall deal was in the non-binding Political Declaration.
The memo shows that within Whitehall, weakening these provisions was a key part of the renegotiation.
Regarded as an internal success, their removal paves the way for a "much more open starting point for future relationship negotiations" that allow for "a range of landing zones" for a future deal.
"The Political Declaration text provides us with a framework for negotiating FTA-style commitments on Level Playing Field," the memo concludes under the headline "Next Steps".
That is a reference to the fact that, unlike the original Brexit deal agreed by Theresa May, dispute settlement mechanisms have not applied to existing standard EU Free Trade Agreements.
Sam Lowe, trade fellow at the Centre for European Reform, said: "The Level Playing Field commitments in the EU's Free Trade Agreements with Canada and Japan are unenforceable, because they are specifically excluded from the dispute settlement mechanisms. The government appears to be aiming for the same treatment."
Speaking on the BBC's Andrew Marr Show on Sunday, Conservative Party chairman James Cleverly rejected suggestions there are attempts to relax workplace rights or environmental protections.
"In many areas we have already gone further than the European Union," he said. "We are making hard improvements on worker rights through an increase in the National Living Wage."
The government was also strengthening rules on maritime protection and animal welfare, he added.
On Saturday, ministers said stories about the leaked memo were "not correct" and "way exaggerated".
The government also said: "The UK government has no intention of lowering the standards of workers' rights or environmental protection after we leave the EU.
"UK level playing field commitments will be negotiated in the context of the future UK-EU free trade agreement, where we will achieve a balance of rights and obligations which reflect the scope and depth of the future relationship."

Former Chancellor Philip Hammond has accused the PM of trying to wreck the chance of a new Brexit deal, by making demands the EU could never accept.
In a Times article, Mr Hammond said a no-deal Brexit would be "a betrayal" of the 2016 referendum result.
He told the BBC he was "confident" that Parliament "has the means" to express its opposition to a no-deal exit.
A No 10 source said the UK would leave on 31 October despite Mr Hammond's "best efforts to the contrary".
The source added that Mr Hammond, as chancellor, "did everything he could" to block preparations for leaving and had "undermined negotiations".
The former chancellor rejected this suggestion in a tweet, saying he wanted to deliver Brexit "and voted to do so three times".
Prime Minister Boris Johnson has said he wants to leave the EU with a deal, but the UK must leave "do or die" by the latest Brexit deadline of 31 October.
He wants the EU to ditch the Irish border backstop plan from the deal negotiated by former PM Theresa May, which was rejected three times by Parliament.
But the EU has continued to insist that deal, including the backstop arrangements, is the only agreement possible.
Many of those who voted against the deal had concerns over the backstop, which if implemented, would see Northern Ireland staying aligned to some rules of the EU single market.
It would also see the UK stay in a single customs territory with the EU, and align with current and future EU rules on competition and state aid.
These arrangements would apply unless and until both the EU and UK agreed they were no longer necessary.
Speaking on BBC Radio 4's Today programme, Mr Hammond said a no-deal exit would be "just as much a betrayal of the referendum result as not leaving at all".
He said that Mr Johnson's demand for the backstop to be entirely removed from the deal meant a no-deal was inevitable on the current 31 October deadline.
He said that agreeing to changes now would "fragment" the EU, adding: "they are not going to take that risk".
"Pivoting to say the backstop has to go in its entirety - a huge chunk of the withdrawal agreement just scrapped - is effectively a wrecking tactic," he said.
He also told Today that he was "very confident" MPs would be able to pass legislation to express their opposition to a no-deal exit.
However he said he did not favour the tactic of replacing the PM with a national unity government designed to prevent no deal, saying: "I don't think that's the answer".
In his Times article, Mr Hammond said "the unelected people who pull the strings of this government know that this is a demand the EU cannot, and will not, accede to."
BBC political correspondent Tom Barton said that remark was an apparent aim at the prime minister's closest adviser, Dominic Cummings - the former Vote Leave campaign director.
It was a "travesty of the truth", Mr Hammond wrote, to pretend that Leave voters backed a no-deal Brexit in the 2016 referendum.
But Leave-supporting former Tory leader Iain Duncan Smith, also speaking on the Today programme, said he was "astounded" by Mr Hammond's remarks.
"Talk about hubris. This man did nothing to prepare us for leaving with no deal," he said.
"The fact we are now doing that means we have a much better chance to get some kind of agreement from them because they now know we're going to leave with no deal and he's undermining that."
Mr Hammond's comments come as Downing Street said it expected a group of MPs to try to block a no-deal Brexit by attempting to pass legislation when Parliament returns next month.
The Daily Telegraph reports that Commons Speaker John Bercow told an audience at the Edinburgh Fringe festival that he "strongly" believes the House of Commons "must have its way".
He said he would "fight with every breath in my body" any attempt by the prime minister to suspend Parliament to force through a no-deal against MPs' wishes.
On Tuesday, Work and Pensions Secretary Amber Rudd urged Mr Johnson not to force through a suspension.
She told the BBC: "I remain a great admirer of Parliament and of parliamentary sovereignty and I will continue to argue for the executive of the government that I'm part of to work with Parliament, not against them."
Meanwhile, 20 other senior Tory MPs have written to the prime minister to say his demand to scrap the Irish backstop "set the bar so high that there is no realistic probability of a deal being done".
The MPs said they were "alarmed by the 'Red Lines' you have drawn which, on the face of it appear to eliminate the chance of reaching agreement with the EU".
The group also demands that Mr Johnson declares he is firmly committed to leaving the EU with a deal and is ready to compromise to get one - pointing out those were assurances he gave during the leadership campaign "both publicly and privately".
Seven other former cabinet ministers have signed the letter, including David Lidington, David Gauke, Rory Stewart and Greg Clark, all of whom resigned before Mr Johnson took office.

A no-deal Brexit poses a risk to the public because the UK would lose access to EU-wide security powers and databases, police leaders have warned.
Police and crime commissioners say law enforcement agencies "face a significant loss of operational capacity" if the arrangements stop.
They have asked the home secretary to confirm his contingency plans.
The Home Office says it will continue to make the case for the retention of the capabilities.
In a letter to Home Secretary Sajid Javid, the Association of Police and Crime Commissioners' cross-party Brexit Working Group stresses the importance of continued co-operation with European policing and justice bodies after March 2019.
It says 32 measures are currently being used on a daily basis including the European Arrest Warrant;  the Schengen Information System -  a database of "real time" alerts about certain individuals - and the European Criminal Records Information System.
"The UK and EU share a common and ever evolving threat picture. We believe that a comprehensive partnership in all areas of policing and security co-operation is of mutual benefit to all," they add.
The commissioners say after discussions with National Crime Agency and the National Police Chiefs' Council, they understand "considerable additional resource would be required for policing to operate using non-EU tools and that such tools would be sub-optimal - potentially putting operational efficiency and public safety at risk".
They add: "We are therefore concerned that a 'no deal' scenario could cause delays and challenges for UK policing and justice agencies."
The EU's chief negotiator Michel Barnier has indicated the UK would not be able to remain part of the European Arrest Warrant after Brexit and said it would not have the same access to organisations such as police agency Europol.
But in June, the prime minister complained EU negotiators were blocking agreement on deals, risking the safety of EU and UK citizens.
A Home Office spokesman told the Guardian: "There is widespread recognition that the UK and EU can most effectively combat security threats when we work together.
"It is important we maintain operational capabilities after Brexit, and we will continue to make this case to the European Commission."
He said the government was confident co-operation would continue but it was also preparing for "every eventuality, including no deal".

The Scottish National Party is calling on Labour to work with other opposition parties to keep Britain in the single market and customs union after Brexit.
Its Commons leader Ian Blackford asked for help to stop the "catastrophic damage" of "extreme" Brexit.
"It is time for MPs of all parties to put politics aside," he said.
Labour says the UK should "stay aligned" to the EU after Brexit and could pay to access the single market like Norway.
Mr Blackford said he would invite other opposition leaders to a summit on 8 January when MPs return from the Christmas recess.
He said: "As we saw with the successful amendments to the EU Withdrawal Bill, when opposition parties work together effectively it is possible to secure a parliamentary majority and deliver change in the national interest."
The SNP, Liberal Democrats, Plaid Cymru and the Greens have all said they want the UK to stay in the single market and customs union after Brexit - something Prime Minister Theresa May has already ruled out.
Labour's leader, Jeremy Corbyn, has also faced criticism over his refusal to support a second referendum on the final terms of the UK's exit from the EU.
He told the i newspaper: "We have had a referendum which came to a decision. The negotiations are still ongoing, albeit well behind schedule, and we've set out the kind of relationship we want to have with Europe in the future."
Tom Brake, Brexit spokesman for the Liberal Democrats, said the Labour leadership had "shirked their responsibility" to provide effective opposition to the government.
"The Labour leadership has constantly played a game of smoke and mirrors over their Brexit position.
"But here they are nailing their colours to the mast in support of hard Brexit," he added.

Theresa May will update MPs on Tuesday about recent Brexit talks as she continues to seek support for her deal.
She visited Dublin and Brussels last week seeking EU agreement on changes to the backstop - the "insurance" policy to avoid the return of visible Northern Ireland border checks.
Last month MPs - who will debate Brexit on Thursday - voted for the PM to find alternatives to the current backstop.
But the EU has said it would not renegotiate the withdrawal agreement.
However, efforts to come up with a solution acceptable to both sides continue.
Brexit Secretary Steve Barclay met a group of Tory MPs working on possible alternatives to the backstop, before he travelled to Brussels and held talks with EU negotiator Michel Barnier.
Following the meeting, Mr Barnier said the talks had been "constructive", but added it was "clear from our side we're not going to reopen the withdrawal agreement, but we will continue our discussions in the coming days".
A statement from the Department for Exiting the European Union said Mr Barclay and Mr Barnier had agreed to further talks "in the coming days". Their teams would continue to work in the meantime "on finding a way forward", it added.
The statement to the House of Commons on Tuesday - a day earlier than had been expected - follows an exchange of letters between Mrs May and Jeremy Corbyn.
The Labour leader wrote to the PM on Wednesday with a list of five demands to secure his party's support for her deal, including a permanent customs union.
The prime minister struck a conciliatory tone in her response overnight and said she looked forward to the two parties meeting again "as soon as possible" to discuss ways forward on Brexit.
But No 10 said it rejected any proposals to remain in a customs union with the EU.
Some of her cabinet members also quashed the idea, with International Trade Secretary Liam Fox calling Mr Corbyn's proposal a "dangerous delusion".
Mrs May told the Labour leader: "It is good to see that we agree that the UK should leave the European Union with a deal and that the urgent task at hand is to find a deal that honours our commitments to the people of Northern Ireland, can command support in Parliament and can be negotiated with the EU - not to seek an election or second referendum."
This is despite Mr Corbyn repeatedly saying there should be a general election if Mrs May cannot get a deal through Parliament. He has also faced pressure from some of his MPs to push for another public vote on Brexit.
Shadow Brexit Secretary Keir Starmer said his "key question" about Mrs May's response was: "Is she prepared to move her red lines and find a consensus?"
"I don't see that in the letter," he said.
"The point of the exercise was to say, look, there is a majority for a close economic relationship, if you're prepared to try to find it, and I've said for some time we should test that by having a vote on a customs union."
Labour MP David Lammy - who supports the "People's Vote" campaign for a new referendum - said Mrs May's letter "makes it clear there is no hope of her agreeing" with Mr Corbyn's demands and said his party should campaign now for a fresh vote.
But fellow Labour MP Lisa Nandy told the BBC's Politics Live that there were between 40 and 60 of her colleagues "who are actively looking for ways to support" a revised Brexit deal.
She said the government needed to "get serious" about policy on a customs union and guarantee to "legislate for the protections around workers' rights".
The anti-Brexit Liberal Democrats said it was "astonishing" the two leaders were starting "serious discussions about delivering disastrous Brexit together" 900 days after the vote to leave the EU.
Brexit spokesman Tom Brake added: "It is time for Jeremy Corbyn to give up the letters and instead draw his attention to Labour Party policy and get behind the campaign for a People's Vote."
The GMB union criticised the government's "dangerous brinkmanship" after Mrs May rejected remaining in a customs union. It has urged the extension of Article 50 - the mechanism by which the UK is set to leave the EU on 29 March.
Meanwhile, speaking in Luxembourg, Mr Barnier said he would judge how interested the UK was in changes to the accompanying political declaration, which sketches out the shape of the future relationship.
He said the EU was waiting for a clear and stable majority to emerge in the House of Commons, not just for the passage of the withdrawal agreement, but for the subsequent legislation too.
Mr Corbyn's letter to the prime minister was "interesting in tone and substance", Mr Barnier said.
Elsewhere, members of the Alternative Arrangements Working Group - including Conservative MPs Steve Baker, Marcus Fysh, Owen Paterson, Damian Green and Nicky Morgan - met government officials in Westminster.
Mr Baker said the talks had been "constructive" and they were "looking forward to hearing how Stephen Barclay gets on with Michel Barnier".
The group has met several times to discuss alternative arrangements to the proposed Irish border "backstop".
By Norman Smith, BBC assistant political editor
It could have been a very different sort of letter.
Mrs May could have just underscored her red lines: No to extending Article 50. No to another referendum. No to a customs union.
Instead, it's a much more conciliatory and consensual letter.
There's praise for Mr Corbyn in accepting the priority now should be on reaching a Brexit deal, rather than pressing for a general election.
Praise too for his acknowledgement that the backstop has got to be changed.
And there's some movement on employment rights and the promise of more cash for hard pressed communities.
Even on the customs union - their key dividing area - Mrs May's language is more nuanced, even though privately her aides insist there can be no question of accepting a permanent customs union.
It's unlikely to be anywhere near enough to win over Mr Corbyn.
But it may be enough for those Labour MPs in leave supporting constituencies, who are looking for political cover to back or abstain on Mrs May's deal.
In his letter, Mr Corbyn asked for five changes to be made to the Brexit deal.
The Labour leader called for a "permanent and comprehensive UK-wide customs union" with the EU to be introduced to the deal, with the same external tariff.
He said it would give the UK a say on any future trade deals that the EU may strike.
In her reply, Mrs May said the political declaration - the second part of her deal which is a non-legally binding statement on the future relationship between the UK and EU - "explicitly provides for the benefits of a customs union", with no tariffs, fees, charges and restrictions.
But, she said, it also allows for the UK to strike up its own trade deals elsewhere.
She added her reassurance that securing frictionless trade with the EU was "one of our key negotiating objectives".
Speaking in Switzerland, where Mr Fox has just signed a deal to see the country trade with the UK on the same terms it does now, the minister said the idea was "not workable".
Mr Corbyn also wanted the deal to include a promise for the UK to be closely aligned with the Single Market after it leaves the EU, "underpinned by shared institutions and obligations".
Mrs May quoted the EU as saying the current deal provides for the closest relationship possible outside the Single Market.
She added: "I am not sure what exactly you mean when you say 'shared institutions and obligations', but our teams can explore that."
The PM also repeated the EU's warning that completely frictionless trade is only possible if the UK stays in the Single Market.
"This would mean accepting free movement, which Labour's 2017 General Election manifesto made clear you do not support," she added.
Labour has called for the UK to stay in step with the EU on rights and protections for workers, which was included in Mr Corbyn's letter.
On this point, Mrs May said the government had already made commitments on workers' rights, adding: "We are examining opportunities to provide further financial support to communities that feel left behind."
This could be referring to proposals that were said to have been discussed earlier this month from a group of Labour MPs in predominantly Leave-supporting constituencies, to allocate more funds to their communities for big infrastructure projects.
The PM also said that while she had "always been clear that Brexit should not be at the expense of workers' rights or environmental protections", she did not support automatically following EU rules in these areas.
The Labour leader called for a promise to participate in EU agencies and funding programmes on the environment, education and industry regulation after Brexit.
The prime minister said the government supports participation in EU programmes in a number of areas, as set out in the political declaration - which includes areas such as science and innovation, youth, culture and education, and overseas development.
Finally, Mr Corbyn demanded agreements with the EU on security, such as access to the European Arrest Warrant database.
Mrs May said the government "shares your ambition in relation to security arrangements".
She said the political declaration secured agreement on the exchange of Passenger Name Record, DNA, fingerprint and vehicle registration data and on arrangements "akin to the European Arrest Warrant to surrender suspected and convicted persons efficiently and expeditiously."
But, she added, there is a challenge that as a third country outside of the EU, there are restrictions on the UK's ability to participate in some EU tools and measures.
Labour is yet to respond to the letter.

The government has granted a two-week extension in the process to decide who will make UK passports after Brexit.
British company De La Rue - which had lost the £490m contract to French-Dutch Gemalto in March - had requested the longer "standstill period", which has now been agreed by the Home Office.
It means a final decision will now be made on Tuesday 17 April.
De La Rue is also taking initial steps "towards initiating appeal proceedings against the provisional decision".
However, it has refused to clarify what this means legally or how any appeal process might proceed.
The firm says the time extension will give it more time for close scrutiny of the criteria that the Home Office used in coming to its decision to award the contract to Gemalto.
It says it will assess that information and whether it might help it in its arguments.
De La Rue's bid was not the cheapest, but it said it was "the highest quality and technically most secure".
"We have a preferred bidder, which demonstrated it was best able to meet the needs of the passport service, delivering a high quality and secure product and providing best value for money for the taxpayer… that remains the government's position," said the prime minister's official spokesman.
But the extension "will give all bidders the chance to find out more detail and get more information from the Home Office… this is standard process."
The spokesman added: "This has been a rigorous, fair and open process."
The current EU-themed burgundy passport, in use since 1988, will revert to its original blue and gold colour from October 2019. However, people are expected to keep their current passports until they expire.
Before the bidding process extension, a spokesperson for De La Rue had said: "We can accept that we weren't the cheapest, even if our tender represented a significant discount on the current price.
"It has also been suggested that the winning bid was well below our cost price, which causes us to question how sustainable it is."
The decision to give a foreign company the contract had been criticised by pro-Brexit government figures.
Under EU procurement rules, the Home Office was required to open up the bidding process to European firms, although De La Rue has manufactured UK passports since 2009.
The Home Office had said the proposed Gemalto deal could save the taxpayer £100m-£120m and that 70 new jobs would be created in the UK, at sites in Fareham, in Hampshire, and Heywood in Lancashire.
It comes as a Daily Mail petition calling for the Home Office to give the contract to a British firm reached 273,000 signatures.
The Home Office issues more than six million passports annually and is the only provider of passports to British citizens.

The EU's negotiator says he is worried by the UK's post-Brexit proposals for the Northern Ireland border.
Michel Barnier said the UK was asking for EU laws, its customs union and single market to be suspended at a "new external border".
He said the UK wanted Northern Ireland to be a "test case" for future customs arrangements with the EU.
The UK said both sides were "closely aligned" in what they wanted to achieve.
Northern Ireland is the only part of the UK that will share a land border with an EU state after Brexit.
The impact of Brexit on Northern Ireland and the Republic of Ireland is one of the key issues being discussed in the early stages of UK-EU negotiations.
Fears have been raised that a return to border checks could undermine the Good Friday peace agreement and damage the economy.
The UK - which plans to leave the EU's customs union - has said it wants an "unprecedented solution", avoiding physical checks at the border.
Instead, the government is arguing for a wide-ranging exemption under which small and medium-sized businesses would not have to comply with any new customs tariffs.
Unveiling the EU's position, Mr Barnier said: "What I see in the UK's paper on Ireland and Northern Ireland worries me."
He added: "Creativity and flexibility can't be at the expense of the integrity of the single market and customs union.
"This would be not fair for Ireland and it would not be fair for the European Union."
Mr Barnier said the peace process should be preserved, the common travel area between Ireland and the UK protected and that there should be no return to a "hard border", all of which the UK has also said it is seeking.
"Irish citizens in Northern Ireland must continue to enjoy their rights as EU citizens," Mr Barnier continued, calling for the UK to come up with a "unique" solution.
As the UK had chosen to leave the EU, it was its responsibility to come up with solutions, he said.
The UK government, which released its own position paper on Northern Ireland last month, said there was now a "good basis on which to continue to make swift progress" on the subject.
It welcomed the EU's view there should be no "physical infrastructure" at the border, but added that "unilateral UK flexibility will not be sufficient to meet our shared objectives".
Brussels has refused to discuss the UK's future relationship with the EU - notably how they will trade with each other - until the initial discussion issues, including Northern Ireland, have been settled.
The EU's paper suggests specific provisions being written into the final departure deal to protect cross-border co-operation in areas like health, education, transport and fishing.
The Liberal Democrats said the EU's document "demolishes another of the Leave campaign's fantastical claims - that Brexit would have no impact on the Irish border".
MP Tom Brake said the only solution to the border question was for the UK to stay in the single market and customs union.
Unveiling the Northern Ireland plans at a press conference, Mr Barnier also attacked the UK over one of the sticking points in the Brexit negotiations - the size of any "divorce" bill required as it leaves the EU.
The UK has said it will honour its financial commitments but also that it has a "duty to our taxpayers" to "rigorously" examine the EU's demands.
Mr Barnier said Brussels expected Britain to deliver on commitments made in the multi-year EU budget signed up to by David Cameron and approved by the Westminster Parliament.
"I have been very disappointed by the UK position as expressed last week, because it seems to be backtracking on the original commitment of the UK to honour its international commitments, including the commitments post-Brexit," he said.
"Every euro spent has a specific legal base," he added.
"There is a moral dilemma here. You can't have 27 paying for what was decided by 28. What was decided by the 28 member states has to be borne out by 28 member states, right up to the end. It's as simple as that."
Mr Barnier was also asked about comments which have emerged by European Commission president Jean-Claude Juncker about Brexit Secretary David Davis.
In newly-published minutes of a 12 July meeting between Mr Juncker and Mr Barnier, Mr Juncker was recorded as questioning the "stability and accountability" of Mr Davis.
Mr Juncker also said Mr Davis's "apparent lack of involvement... risked jeopardising the success of the negotiations".
In the meeting, which came after the first round of negotiations, Mr Barnier was recorded as saying the UK negotiating strategy involved "using past debts as a means of buying future access to parts of the single market, something which the Union could not accept".
Mr Barnier brushed off the comments at a Brussels press conference, insisting he had "cordial" relations with the Brexit secretary and praising his "professionalism".
And the Department for Exiting the European Union responded: "These are clearly out-of-date comments and it is abundantly clear that the secretary of state has been fully engaged and involved throughout the discussions, in the same way as Mr Barnier."
In another position paper from the EU, it called for the UK to continue to honour the protected legal status given to delicacies like Parma ham or Champagne after Brexit.
The European Commission first acted in 1992 to establish a list of products which could only be described by their place of origin if they really were produced in that place.
It also includes UK products like Cornish clotted cream, Dorset Blue cheese, and Jersey Royal potatoes.
Under the EU's intellectual property proposals, the UK would implement the "necessary domestic legislation providing for their continued protection".
The impact of Brexit on food was also considered in the House of Commons, where Labour's Jenny Chapman warned against imposing tariffs on European food imports, and asked whether the government was planning a "return to consuming Spam and tinned peaches".
Brexit Minister Steve Baker assured her this was not the case and described her comments as a "fantastical proposal".

Facebook has suspended a Canadian data firm that played a key role in the campaign for the UK to leave the EU.
The social media giant said AggregateIQ (AIQ) may have improperly received users' data.
It cites reported links with the parent company of Cambridge Analytica (CA), the consultancy accused of improperly accessing the data of millions.
AIQ denies ever being part of CA, its parent company SCL or accessing improperly obtained Facebook data.
The Vote Leave campaign paid AIQ £2.7m ($3.8m) ahead of the 2016 EU referendum.
An ex-volunteer with the campaign has also claimed Vote Leave donated £625,000 to another group to get around campaign spending limits, with most of the money going to AIQ. Vote Leave has denied any wrongdoing.
AIQ's website once quoted Vote Leave chief Dominic Cummings saying: "Without a doubt, the Vote Leave campaign owes a great deal of its success to the work of AggregateIQ. We couldn't have done it without them." The quote has since been removed.
In total, AIQ was given £3.5m by groups campaigning for Brexit, including Vote Leave, the Democratic Unionist Party and Veterans for Britain. The UK's Electoral Commission reopened an investigation into Vote Leave's campaign spending in November.
"In light of recent reports that AggregateIQ may be affiliated with SCL and may, as a result, have improperly received FB user data, we have added them to the list of entities we have suspended from our platform while we investigate," a Facebook spokesperson said.
"Our internal review continues, and we will co-operate fully with any investigations by regulatory authorities."
In a message posted to its website, AIQ says it is "100% Canadian owned and operated" and "has never been and is not a part of Cambridge Analytica or SCL".
It adds: "Aggregate IQ has never managed, nor did we ever have access to, any Facebook data or database allegedly obtained improperly by Cambridge Analytica."
It also denied ever employing Chris Wylie, the Canadian whistleblower who alleged that the data of 50m people was improperly shared with Cambridge Analytica. Facebook has since said the number of people affected could be closer to 87m. CA says it obtained the data of no more than 30m people and has deleted all of it.
Analysis by technology correspondent Rory Cellan-Jones
It was three weeks ago that Facebook suspended Cambridge Analytica just hours before a whistleblower's revelations to the Observer newspaper triggered the current scandal over improper use of data.
Christopher Wylie insisted that Aggregate IQ was closely linked to Cambridge Analytica, and supplied documents to the Department for Digital, Culture, Media and Sport select committee which he said proved it.
Now Facebook's decision to suspend the Canadian firm from its platform appears to give further validation to Mr Wylie's claims. It also throws the spotlight back onto the potential use of Facebook data during the Brexit campaign.
Facebook says it is looking into whether the data that Cambridge Analytica acquired improperly from as many as 87 million people - 1 million of them in the UK - ended up with Aggregate IQ. The firm worked for both Vote Leave and BeLeave during the EU referendum campaign, but has always insisted it has never been a part of Cambridge Analytica, and has not had access to any of its Facebook data.
AIQ is a small company operating out of Victoria, British Columbia. It uses data to help micro-target voters and was founded by two Canadian political staffers.
Apart from its Brexit work the company has also been accused by Mr Wylie of distributing "incredibly anti-Islamic" content on social media ahead of the 2015 Nigerian presidential election to discredit Muslim opposition candidate Muhammadu Buhari, who went on to win the contest.
The BBC has approached AIQ for a response to the Nigeria allegations.
Mr Wylie has said that AIQ was referred to among Cambridge Analytica staff as "our Canadian office". He told the Guardian he helped to set up the firm as a "Canadian entity for people who wanted to work on SCL projects who didn't want to move to London" and that he had known the firm's co-founder, Jeff Silvester, since he was 16.
AIQ says it "has never entered into a contract with Cambridge Analytica" and that "Chris Wylie has never been employed by AggregateIQ".
Cambridge Analytica is at the centre of a row over whether it used the personal data of millions of Facebook users to sway the outcome of the US 2016 presidential election and the UK Brexit referendum.

The Irish government has said Brexit trade deal talks should not proceed until there is a firm commitment to preventing a "hard" Irish border.
Taoiseach (Irish Prime Minister) Leo Varadkar said the assurance must be written down before the talks move on.
"Before we move to phase two talks on trade, we want taken off the table any suggestion that there will be a physical border," Mr Varadkar said.
He was speaking at a European summit, attended by Prime Minister Theresa May.
Mrs May's spokesperson said both leaders had agreed to work together to find solutions ensuring there is "no return to the borders of the past".
But Sammy Wilson from the Democratic Unionist Party (DUP) accused the Irish government of trying to "keep the UK chained to the EU".
Earlier, Mr Varadkar's message was echoed by Irish Foreign Minister Simon Coveney, who held talks with his UK counterpart, Boris Johnson, in Dublin.
Mr Coveney said there was "a sense of jumping into the dark" for Ireland, as the future operation of its border with Northern Ireland had not been agreed.
"Yes, we all want to move onto phase two of the Brexit negotiations, but we are not in a place right now that allows us to do that," the foreign minister said.
The UK is due to leave the EU in March 2019, but Mr Coveney suggested the exit process could take up to five years.
In response, DUP MP Sammy Wilson claimed the Irish government was "fully signed up with the European establishment to thwart the referendum result in the UK to leave the EU."
In a statement, the MP accused Irish ministers of "trying to block the UK moving on to substantive negotiations about leaving the EU, and then suggesting that an interim or transitional period of five years is going to be needed before we can leave".
"The objective is quite clear; keep the UK chained to the EU until after the next election, when the Irish government hope that Corbyn's Brexit-breaking MPs might be in power," Mr Wilson added.
He said it seemed like the Irish government were content to involve themselves in the affairs of another state.
The MP for East Antrim said that the DUP will support the passing of legislation which would mean "deal or no deal, the UK will exit the EU in March 2019".
Despite cordial exchanges between the two foreign ministers, one thing was clear: Ireland and the UK are still at odds about whether enough progress has been made in the EU-UK divorce talks to allow the two sides to move onto discussions about future relationships.
Despite British assertions that there will be no hard border on the island of Ireland, Dublin doesn't see how that position can be married with the UK leaving the customs union and the single market.
Nor does Dublin think a two-year transitional deal for business to adjust to Brexit is long enough.
With Taoiseach Leo Varadkar delivering the same message to Theresa May in Sweden, there is a sense that "make-your-mind-up time" for all sides is fast approaching.
During his talks in Dublin, Mr Johnson said it was necessary to move on to the second stage of negotiations, where issues raised by Mr Coveney would be thrashed out.
"Now is the time to make haste on that front," the UK foreign secretary said.
Mr Coveney said he understood the British "aspiration" to avoid a hard border, but more clarity was needed about the future.
"We are in the heat of the negotiations right now and, of course, we want to move on to the negotiations on trade, but there are issues that need more clarity," he said.
"This is a very fundamental change in the relationship between Ireland and Britain and Britain and the EU and it will require significant adjustment.
"The appropriate timetable is closer to four or five years than it is to two."
Mr Coveney added: "We simply don't see how we can avoid border infrastructure.
"Once standards change it creates differences between the two jurisdictions and a different rule book.
"When you have a different rule book you are starting to go down the route of having to have checks."
Asked whether the government was constrained by its confidence and supply arrangement with the Democratic Unionist Party, Mr Johnson said that was "not at all an issue".
The DUP agreed to support Theresa May's minority government after June's election in return for £1bn of extra funding for Northern Ireland.
European leaders say talks can only progress if enough progress has been made on the Irish border, citizens' rights and Britain's EU budget contributions.
Meanwhile, Ken Clarke has said the UK remaining in the single market and customs union is vital for peace and stability in Northern Ireland.
It is the obvious solution as no-one wants physical border controls, the former chancellor and now Conservative "rebel" told BBC NI's The View.
"The border problem in Northern Ireland, the supreme importance of keeping the settlement in place, retaining peace in Northern Ireland is probably the single biggest, most important reason why it would be preferable for the United Kingdom as a whole to stay in the single market and the customs union," he said.
"If the Brexiteers, these right-wing nationalists, won't allow us to do that then the best solution after that, I agree with the taoiseach actually, is to have a border down the Irish Sea."

A former Conservative minister has compared Theresa May's Brexit plan to a "ghastly cockroach" and vowed to vote against it in Parliament.
Owen Paterson said the package agreed at Chequers in July would hamper the UK's ability to negotiate free trade deals with other countries.
Senior ministers have been defending the plan, which Eurosceptics say will keep the UK shackled to EU rules.
The chancellor said it "delivers on the decision of the British people".
Speaking at the Conservative Party conference in Birmingham, Philip Hammond dismissed EU warnings the model would not work, saying: "That's what people said about the light bulb in 1878."
But Mr Paterson, the former Northern Ireland secretary, dismissed it when he appeared alongside other Eurosceptic Tories at a conference fringe event.
The UK should be "actively negotiating" free trade deals with the likes of the United States, he said, but "while Chequers is floating around, like some ghastly cockroach, crawling forwards... they're not going to start talking to us.
"It's absolutely pointless."
He added: "My whip is here taking notes and so I'll say it to him directly - I'm voting down Chequers."
Also on day two of the Tories' conference, three serving EU ambassadors to London publicly criticised Foreign Secretary Jeremy Hunt for comparing the European Union to the Soviet Union.
Mr Hunt had accused Brussels of seeking to "punish" Britain for wanting to leave the EU and compared it to the USSR trying to stop its citizens leaving.
Ambassadors from Estonia, Latvia and Sweden all tweeted their disapproval, with the tweet from the Latvian ambassador being retweeted by the EU Commission's deputy chief negotiator, Sabine Weyand.
Earlier Brexit Secretary Dominic Raab told the EU to "get serious" if it wants a Brexit deal, warning the UK may have "no choice" but to leave without one.
And Mr Hammond hit back at former foreign secretary Boris Johnson, who has led criticism of the Chequers proposals, saying he was a "big picture man" whereas what was needed was "a very detailed and complex negotiation".

Brexit. It's all about Britain, right?
Well, not entirely.
There is the rest of the club to consider - what has become known, rather inelegantly, as the EU-of-27.
They are about to lose - depending on your point of view - a curmudgeonly whinger who was dragging the whole project down or one of their largest economies and the most powerful defence and security power in Europe.
So what to do?
There are those who think, genuinely, good riddance.
"General de Gaulle was right all along," they mutter. "We should never have let them join in the first place.
"Freed from the shackles of British ministers objecting to integration here and integration there, we can get on with it."
Closer co-operation on EU defence policy is high on their list; and it has been given an extra boost by the new president of the United States musing out loud about Nato and whether it is all worth it.
Others are dismayed by the British decision to leave, but after getting over the initial shock - and it really was a shock - they too are determined to make the best of it.
And when it comes to negotiating the UK divorce bill, make no mistake. For the people who matter, the unity of the remaining 27 is more important than trying not to upset the Brits as they wave goodbye.
The bill will be big - up to 60 billion euros - and European diplomats are bracing themselves for what one called "the very real possibility" that the UK will walk out in a huff.
But the likelihood is that after one too many late-night summits - and one too many outraged tabloid headlines - a deal of sorts will emerge from the rubble.
The consequences of Brexit will rumble on for years; there are trade deals that will have to be done. But the EU is in no position to wait for the dust to settle.
In many ways, it has already moved on. So long Britain, and thanks for the memories.
Later this month, leaders of the 27 (the 28th has already sent her apologies) will meet in Rome to celebrate the 60th anniversary of the EU's founding treaty.
I say celebrate, but there is no illusion about the challenges facing the union.
Could the forces that prompted Brexit spread to other countries? Will anti-EU populists continue to rise in France, the Netherlands and parts of Central Europe?
It is certainly not impossible, and EU leaders know it. The idea that the EU could fall apart - unthinkable a few years ago - is now the subject of serious discussion.
Which is why they need a new plan to reinvigorate the project on its 60th birthday, and make it fit for future purpose.
The European Commission has now produced a series of policy options for the best way forward, ranging from shrugging its shoulders to throwing up its hands in horror.
But the most likely solution is to make more use of what is known as multi-speed Europe.
That's the idea that "coalitions of the willing" can move forward on big projects even if others want to linger on the starting line.
It is already happening with the euro, and with the passport-free Schengen area - not all EU countries are members of everything. An inner core may want to push ahead, if (and it's a big if) it can take public opinion along for the ride.
The other Commission proposal that looks to have legs is the idea that Brussels would return some powers to member states, as long as the EU was given greater responsibilities in major policy areas such as trade, migration, security and defence.
Variations on this theme have been around for some time. The EU needs to be big on the big things, they said, and smaller on smaller things.
And the biggest of the big things - in a competitive field - is probably the need to fix the eurozone.
The single currency remains half-formed, and - as a result - not yet secure. There is talk of a eurozone finance minister and a single eurozone budget.
But if you centralise economic power, you have to make sure it is politically accountable.
In an era of populist, anti-establishment rage, that is a difficult balancing act. Much will depend on who wins national elections this year in Germany and, in particular, France.
Political leadership will be at a premium.
But as the UK prepares to leave and enter a whole new world, the status quo is no longer an option for the countries that remain.
The EU either needs to move forward towards closer integration, or transfer significant power back to nation states.
It continues to be a bold experiment in Europe. But the halfway house has been built on sand.

Michel Barnier has dismissed Boris Johnson’s Brexit proposals to replace the Irish border backstop as a “trap”.
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The EU negotiator warned a group of senior MEPs that the EU could be locked into a string of commitments if the measure vetoed by the Northern Ireland Assembly. According to a source in the meeting, he said: “The EU would then be trapped with no backstop to preserve the single market after Brexit.” European officials are concerned that the Prime Minister’s demand for a “firm commitment by both parties to never conduct checks at the border in future” would leave the EU powerless to protect its single market if the DUP rejects the backstop.
Guy Verhofstadt, the EU Parliament’s Brexit co-ordinator, said he was “absolutely not positive about Johnson’s proposals”.He added: “It doesn’t provide the necessary safeguards for Ireland.”Jean-Claude Juncker, the European Commission’s President, said the UK plan to offer the DUP a veto is “problematic” but promised to work through the issue.Senior EU diplomats have said giving such an influential role to Stormont is “unacceptable”.
Mr Barnier has pleaded for “more time” to look at the proposals before they are rejected out of hand by other EU figures.During private meetings, his Article 50 task force told diplomats that the backstop proposals don’t meet the three necessary criteria.Officials warned claimed proposals don’t protect the EU’s single market, the Good Friday Agreement and questioned whether Mr Johnson can secure a Common’s majority.MUST READ: Queen’s Speech date: When is Queen’s Speech to open Parliament?
EU negotiators also rejected the Government’s request to hold the next round of negotiations in a so-called “tunnel” - a period of secret and intense talks.Capitals have already expressed their frustrations at not being allowed access to the 44-page alternative to the backstop.David Frost, the Prime Minister’s top adviser, will resume talks on Friday in Brussels.DON'T MISSBoris Johnson’s most critical error could still cost Britain Brexit [EXCLUSIVE]Varadkar deals major blow to Boris's Brexit plan [INSIGHT]Five reasons Brexiteers can celebrate Boris's Brexit plan – REVEALED [ANALYSIS]
Domestically, Mr Johnson’s proposals have gone down far better.The DUP has signalled it could accept the new system - even though Northern Ireland would align to the EU’s single market rules for agri-food and industrial goods.Steve Baker, chair of the eurosceptic European Research Group, said he would support the new deal if the DUP followed suit.
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“On the union it's clear to me we don't have a right to trump the DUP,” he said.Meanwhile, Mr Johnson announced a short prorogation to hold a Queen’s speech.Parliament will be suspended from next Tuesday until October 14 to allow a new legislative programme to be set.
Brexit has "turned out less badly than we first thought", David Cameron has said.
The former prime minister was recorded at the World Economic Forum in Davos saying the Leave vote was "a mistake not a disaster".
Mr Cameron called the 2016 referendum on the UK's membership of the EU, campaigned to stay in and resigned after the Leave side won.
His apparently unguarded comments were highlighted by Channel 5 News.
"As I keep saying, it's a mistake not a disaster," he was heard saying in a conversation with steel tycoon Lakshmi Mittal.
"It's turned out less badly than we first thought. But it's still going to be difficult."
The Remain campaign during the referendum warned of an immediate economic impact on the UK of a vote to leave the European Union.
In a speech to Vauxhall car workers, in Ellesmere Port, four months before the referendum, he warned voters about the economic shock that he said would be caused by a vote for Brexit.
"Let's just remember what a shock really means. It means pressure on the pound sterling. It means jobs being lost. It means mortgage rates might rise. It means businesses closing. It means hardworking people losing their livelihoods."
He stepped up his warnings as the referendum date approached, warning on 6 June that Brexit would be like putting a "bomb" under the UK economy and telling MPs a week later that "nobody wants to have an emergency Budget, nobody wants to have cuts in public services, nobody wants to have tax increases", but the economic "crisis" that would follow a vote to leave could not be ignored.
"We can avoid all of this by voting Remain next week," he added.
He described a vote to leave the EU as a "self-destruct option" for the UK, after a Treasury analysis warned it would tip the UK into a year-long recession, with up to 820,000 jobs lost within two years.
At other times he sounded more optimistic about the prospect of leaving, saying, in May 2016, "Britain is an amazing country. We can find our way whatever the British people choose."
A leading Brexit supporter, former Conservative and UKIP MP Douglas Carswell, welcomed Mr Cameron's comments.
The BBC's chief political correspondent, Vicki Young, said Tory Brexit cheerleaders she had spoken to were "thrilled", telling her the former PM had come round to their "way of thinking".
But she said one leading Remain campaigner in the party said it was "far too early" to tell what the long-term consequences of leaving the EU would be.
Former Labour MP Gisela Stuart, who now heads pro-Brexit campaign group Change Britain, said the former PM's "scaremongering" about the economic damage of Brexit had proved to be "baseless".
"I hope that pro-EU MPs who continue to do Britain's economy down join Mr Cameron in admitting they're wrong, and focus their energies on getting the best Brexit deal for the UK," she said.
Although the pound fell sharply after the vote, the UK economy has continued to grow, and unemployment has fallen to a 42-year low. Mortgage rates have stayed at generally the same low levels they have been since the financial crisis in 2008.
The UK and the EU are currently negotiating the terms for the UK's exit and future relations, and the date for Brexit has been set for 29 March 2019.

The UK will continue to take part in the Erasmus student exchange programme until at least the end of 2020, the prime minister has said.
Theresa May praised Erasmus+ and confirmed the UK would still be involved after Brexit in March 2019.
Whether it is involved long term is among issues likely to be discussed during the next stage of negotiations.
Erasmus+ sees students study in another European country for between three and 12 months as part of their degree.
The prime minister is in Brussels where she will have dinner with EU leaders on Thursday.
On Friday, without Mrs May, they are expected to formally approve a recommendation that "sufficient progress" has been made in Brexit negotiations so far to move them onto the next stage.
Mrs May agreed a draft deal with European Commission President Jean-Claude Juncker last week which would mean the UK would continue its funding of EU projects, including Erasmus, until the end of this EU budget period in 2020.
If EU leaders approve the draft deal, Brexit negotiations can begin on the next phase, covering the future relationship between the UK and EU and a two-year transition or implementation deal from March 2019. It is not clear whether this would include Erasmus+.
Mrs May said that British students benefitted from studying in the EU while UK universities were a popular choice for European students.
Speaking during a discussion on education and culture at the summit in Brussels, she added: "I welcome the opportunity to provide clarity to young people and the education sector and reaffirm our commitment to the deep and special relationship we want to build with the EU."

The UK has "danced to the EU's tune" during the Brexit negotiations, former UKIP leader Nigel Farage has claimed.
In a debate in Strasbourg, he called the British Prime Minister, Theresa May, "Theresa the appeaser", saying she had "given in on virtually everything".
The European Parliament later voted to endorse an agreement struck by the UK and European Commission which is set to move the talks on to their next phase.
But MEPs also insisted the UK must honour the commitments it has made.
Amid concerns about whether Friday's agreement on citizens' rights, the Northern Ireland border and the so-called "divorce bill" is legally binding, Guy Verhofstadt, the European Parliament's Brexit spokesman, said he had been reassured the UK would not "back-track" on its commitments.
The agreement should be converted into a legal text in weeks, not months, he added.
In a symbolic but politically significant vote, the European Parliament backed the European Commission's view that sufficient progress had been made on so-called divorce issues to move to talks covering a transition phase and the EU's future relations with the UK.
The EU's negotiator  Michel Barnier said there was "no going back" on Friday's agreement - which is expected to be rubber-stamped by all other 27 EU members later this week.
"It has been noted and recorded and is going to have to be translated into a legally binding withdrawal agreement," he said.
During the debate, several MEPs criticised the UK's Brexit Secretary, David Davis, for suggesting in an interview on Sunday that the first-phase agreement was more of a "statement of intent" than a "legally enforceable thing" - comments he has since backed away from.
German Christian Democrat MEP Manfred Weber, who leads the centre-right EPP group, said the remarks were "not helpful" for building trust between the two sides.
Meanwhile, Mr Farage - who has campaigned for 20 years to take the UK out of the EU - also attacked the British government, saying Mr Barnier "didn't need" to make many concessions to Theresa May.
"I'm not surprised you're all very pleased with Theresa the appeaser - who has given in on virtually everything," he said.
"She has danced to your tune all the way through this. You must be very, very happy indeed."
Warning of a further betrayal of Brexit voters, he said the prospect of a two-year transition after the UK left in March 2019 would be the "biggest deception yet", meaning the UK would have left the EU "in name only".
"I think Brexit at some point in the future may need to be refought all over again," he added.
But defending the British prime minister, Conservative MEP Syed Kamall said both sides had needed to make compromises and concessions in order to "avoid a no-deal situation".
Important progress had been made, he added, when both sides "understood the need for flexibility and focused on building a better future rather than looking back at the past".

Theresa May has said the UK is "on course to deliver on Brexit" as she arrived in Brussels, the day after her first Commons defeat as prime minister.
She said she was "disappointed" at the vote on the EU Withdrawal Bill, but the legislation was making "good progress".
MPs backed an amendment giving them a legal guarantee of a vote on the final Brexit deal struck with Brussels.
EU leaders are expected to formally agree to start the next phase of negotiations on Friday.
The European Commission has said "sufficient progress" has been made on the first phase to move onto discussing the framework of a future relationship between the EU and UK - on issues such as security and trade.
Mrs May told fellow EU leaders at dinner on Thursday that she wanted to get agreement on the "implementation period" as a priority but wanted to talk about trade "as soon as possible".
She said was personally committed to delivering a "smooth Brexit" and she wanted to approach the next phase of talks "with ambition and creativity".
Speaking to reporters earlier, she said: "I'm disappointed with the amendment but actually the EU Withdrawal Bill is making good progress through the House of Commons and we are on course to deliver Brexit."
Asked whether she felt she would have to compromise more to win over rebels from her own party, she told BBC political editor Laura Kuenssberg: "We've actually had 36 votes on the EU Withdrawal Bill, and we've won 35 of those votes with an average majority of 22."
Mrs May lost by just four votes, as MPs backed an amendment to the EU Withdrawal Bill by 309 to 305.
Labour leader Jeremy Corbyn described it as a "humiliating loss of authority" for the PM and warned that his party would vote against another bit of the bill - the plan to put a fixed Brexit date into law.
He said setting an "arbitrary date" was not sensible and there "should be some flexibility".
It will not derail Brexit but MPs who voted against the government hope it will give them a bigger say in the final deal Theresa May strikes with Brussels.
BBC Brussels reporter Adam Fleming said that as other EU leaders also run minority or coalition governments they would see the vote defeat as a small-scale domestic political issue.
The government had promised a "meaningful vote" for MPs on the final Brexit deal, but this defeat means that promise now has legal force and must happen before any UK-EU deal is implemented in the UK.
Ministers had wanted to be able to start implementing any deal as soon as it was agreed - in case, for instance, it was only agreed at the last minute.
BBC political editor Laura Kuenssberg said it would embolden the opposition and showed there was a majority in Parliament against a "hard Brexit".
Cabinet Minister Jeremy Hunt told the BBC the vote was "not going to stop Brexit".
Labour joined forces with the SNP, the Liberal Democrats and the Green Party in a cross-party alliance.
If all Conservative and DUP MPs had voted against the amendment the government would have won. But 11 Conservatives resisted the arm-twisting by their party managers to vote with the opposition.
The Tory rebels were Dominic Grieve, Heidi Allen, Ken Clarke, Jonathan Djanogly, Stephen Hammond, Sir Oliver Heald, Nicky Morgan, Bob Neill, Antoinette Sandbach, Anna Soubry and Sarah Wollaston. Another Conservative MP, John Stevenson, officially abstained by voting for and against the amendment.
Two Eurosceptic Labour MPs - Frank Field and Kate Hoey - voted with the Conservatives and the DUP.
Emotions ran high before, during and after Wednesday's Commons debate, with Eurosceptic Conservatives accusing the rebels of trying to "frustrate" Brexit.
In dramatic scenes, the rebels shouted "too late" as Justice Minister Dominic Raab announced a concession shortly before voting began and Tory whips could be seen attempting to twist the arm of MPs thinking of voting against the government.
Leading rebel Anna Soubry said she had found a woman MP "upset and shaken" on Tuesday evening after a whip tried to persuade her not to revolt. She told MPs on Thursday morning, that none of the rebels took any pleasure in defeating the government, adding that "nobody drank champagne".
After the result was announced, one of the rebels, former cabinet minister Nicky Morgan, tweeted: "Tonight Parliament took control of the EU Withdrawal process."
This did not go down well with Tory MP Nadine Dorries, who called for the deselection of rebel Tories for "undermining the PM", and accused their leader, Dominic Grieve of "treachery".
Rebel Tory Sarah Wollaston hit back on Twitter, saying: "Get over yourself Nadine."
Dominic Grieve tried to calm the mood, insisting he was merely trying to ensure Brexit was carried out in an "orderly, sensible way".
BBC political editor Laura Kuenssberg
It's certainly true that the Tory party is so divided over how we leave the EU that the Parliamentary process was always going to be very, very choppy.
But another minister told me the defeat is "bad for Brexit" and was openly frustrated and worried about their colleagues' behaviour.
Read the rest of Laura's blog
Theresa May has travelled to Brussels to attend a dinner with the 27 other EU leaders, at which she will urge them to approve an agreement to move Brexit talks on to a second phase.
They are all but certain to agree.  Talks could then start next month on the two-year transition period the UK wants to ease it out of the EU after it formally leaves in March 2019.
But the EU wants more detail from the UK government before starting talks on a future relations - including trade - with the UK.
Brexit Secretary David Davis has said he wants to complete the "substantive portion" of trade negotiations by March 2019, leaving open the possibility that the detail will be hammered out during the two-year transition period.
The EU Withdrawal Bill is a key part of the government's exit strategy.
Its effects include ending the supremacy of EU law and copying existing EU law into UK law, so the same rules and regulations apply on Brexit day.
MPs have been making hundreds of attempts to change its wording - but Wednesday's vote was the first time one has succeeded.
Unless the government manages to overturn it further down the line, it means a new Act of Parliament will have to be passed before ministers can implement the withdrawal deal struck with Brussels.
Labour's Shadow Brexit Secretary Sir Keir Starmer urged David Davis not to undermine Wednesday night's vote when the EU Withdrawal Bill reaches the next stage of its passage into law.
Mr Davis said the vote would lead to a "very compressed timetable" for Brexit legislation and the government "will have to think about how we respond to it".
There is also a row brewing over a vote next week on putting the precise date and time of Britain's exit from the EU - 11pm on 29 March 2019 - into law.
Sir Keir described the vote as the next "accident waiting to happen", telling Mr Davis: "Rather than repeat last night's debacle, will the government now commit to dropping that ill-conceived gimmick?"
Mr Davis told Sir Keir: "Unlike him, I do not view votes of this House of Commons as accidents. They are decisions taken by the House, and that decision we respect, as we will the next one."
Lib Dem Brexit spokesman Tom Brake also warned the prime minister she was heading for defeat if she did not drop the "silly idea" of enshrining the Brexit date and time in law, adding: "Parliament has now shown it is not prepared to be bullied."


Labour today said it will seek to amend the upcoming vote on triggering Article 50 by demanding MPs be given votes throughout the EU talks. 
It not only threatens to delay Theresa May's timetable for starting Brexit talks but also risks frustrating the entire two-year negotiation with the EU.  
And Jeremy Corbyn also admitted today that Labour MPs will only be 'asked' to vote in favour of triggering Article 50, rather than imposing a three-line whip on his party.
But shadow home secretary Diane Abbott caused further confusion by saying 'we don't know what amendment we're going to move,' before adding: 'But we are clear that we will not vote to bloc it [Article 50].'  

Dozens of pro-Remain MPs pledged to go further than the Labour leadership and vote against starting Brexit talks altogether, despite last June's vote to leave the EU. 
Shadow Chancellor John McDonnell said Labour will demand the Government allow 'full parliamentary scrutiny throughout the process'. 
He wants 'regular statements' from ministers and frequent votes on the Government's progress. He said that would ensure Britain gets the 'compromise that will work' for both Britain and Europe. 
Mr Corbyn said Labour would use the parliamentary vote on authorising Article 50 to be triggered to 'make demands' on access to Europe's single market and protecting workers' rights.
He insisted Labour would not vote against Article 50, the formal mechanism for leaving the EU, but again refused to say if he will order a three-line whip on his MPs. 
Fresh questions were raised today over whether Jeremy Corbyn voted for Brexit. 
John Longworth - the former director of the British Chambers of Commerce who was forced to quit after saying Britain could have a 'brighter future' outside the EU - said the Labour leader was the 'first person' to congratulate him on his speech in March last year. 
Mr Corbyn was attacked for his lack of enthusiasm for the EU during the referendum despite being part of the Remain campaign. He insisted he voted Remain but even some of his own MPs doubt he did. 
Today Mr Longworth said Labour were 'all over the place' on Brexit. 
And he revealed: 'When I made my fateful speech to the British Chambers of Commerce – which led me to resign and fight the campaign to leave – the first person to come up to me in the green room after I'd made the speech and congratulate me, shake my hand and say what a fantastic speech, was Jeremy Corbyn.
'So that tells you exactly where Labour are on this on this issue.'  
Remarkably Ms Abbott said she was unable to say whether Labour would whip the Article 50 vote. 
She told the BBC: 'We are going to amend it. We can only tell you exactly how we’ll amend it when we understand what sort of legislation the government is bringing forward. 
'And in the course of moving those amendments we will ask the questions that the people of Britain, actually, whether they voted Leave or Remain, want answered.
Asked whether there would be a three-line whip on the vote, she answered: 'I can’t tell you what the whipping will be because we haven’t seen the government’s legislation.'
Tory MP Maria Caulfield said today's comments from the Labour leadership was further proof that the Opposition are 'hopelessly divided and confused over how to respond to the referendum result'.
She said: 'They can't agree over whether we should leave the single market, can't say whether they will have an agreed position in Parliament – and have said this morning they will also find new ways of frustrating the process of leaving.
'Labour are flailing about, irrelevant, incompetent and completely out of touch with ordinary working people.'
MPs will be given the final say on triggering Article 50 if the Government loses its appeal in the Supreme Court.
Judges will announce their decision on Tuesday and if the Government loses, as is expected, ministers will present legislation to the Commons to give the Prime Minister the authority to trigger the clause.
A cross-party group of MPs have told the Observer they will amend any Article 50 Bill to make what they call Mrs May's 'extreme Brexit' with no deal impossible.
Former deputy prime minister Nick Clegg told the newspaper he had been talking to MPs from other parties about how to gather support for amendments 'because the situation is so serious we are condemned to work together on amendments that we can all support.'
Prominent Labour parliamentarians such as Lord Hain and Mike Gapes are among those promising to vote against triggering Article 50 and there have been suggestions that dozens of MPs in pro-Remain seats could rebel against the leader over the matter. 
Anti-Brexit campaigner Gina Miller today attacked American tech firms for refusing to hand data to police that could help catch her abusers. 
She said she and her family had received a barrage of death threats since she won her High Court case that ruled the Government could not start Brexit talks without a vote in Parliament.
Ms Miller, the public face of the court case, appeared to single out Facebook for failing to do enough to help police catch internet trolls. 
One opponent posted 'all of my contact details on Facebook so they [the threats] were coming straight to me' she told the BBC today. 
Police have made arrests and have issued six cease and desist letters. 
But Ms Miller said: ‘The problem is that some of it the American technology communication organisations are not great at providing the data they need to track this, which is a big issue in itself so there are 12 or odd cases still being pursued.'
The Government appealed the High Court decision in November that the Prime Minister must win the approval of MPs before triggering Article 50 - the formal mechanism for leaving the EU. 
Supreme Court judges will deliver its verdict on Tuesday.
But the Government expects to lose and ministers have already drafted legislation to rush through Parliament so Theresa May can stick to her timetable of triggering Article 50 by the end of March. 




Meanwhile dozens of Labour MPs have written to the Prime Minister condemning her threat to leave the EU with no trade deal.
Mrs May insisted in her speech last week that she will walk away from negotiations with Brussels if she is only offered a bad deal, threatening to adopt a Singapore-style low-tax, low-regulation economic model to maintain competitiveness.
The group of Labour MPs have attacked Mrs May's idea, saying it would make Britain 'the sweatshop of Europe' with public services, workers' rights and environmental protections all at risk.
The letter was organised by senior Labour MP Chuka Umunna, who chairs Vote Leave Watch and said he would not rebel against Jeremy Corbyn over triggering Brexit. 
Mr Umunna said: 'Personally, as a democrat and having agreed to the rules under which the referendum was fought, I would find it hard to vote against triggering Article 50.
'But the content of the Brexit deal is a different matter - I am not prepared to give the Tories a blank cheque to make life harder for middle and lower income households in my constituency, a sentiment which is shared across the House of Commons.'
The signatories include former deputy Labour leader Harriet Harman, two members of the current Labour frontbench, 10 former members of the shadow cabinet, and 15 MPs whose constituencies voted to leave the EU. 
Meanwhile, shadow Brexit secretary Sir Keir Starmer said he would fight any attempts to water down human rights or environmental protections once the UK leaves the EU.
The so-called 'Great Repeal Bill', which transposes all EU law into UK law, giving Parliament the power to decide which bits to keep, could include a 'Henry VIII clause' allowing ministers to ditch or change sections through secondary legislation with minimal scrutiny by MPs.

That is because it the Bill is expected to pass before the Prime Minster concludes a final Brexit deal with the Government.
Sir Keir said Labour would fight against any attempts to push through changes without full parliamentary approval.
He told the Independent: 'It would be wrong for these rights to go into our law and then be capable of being amended or removed by statutory instrument.
'I think that's a really important principle that we must fire to the beginning of any discussion on the Great Repeal Bill.' 
 
As a proud member of Her Majesty’s Press, I am reluctant to admit this: but yesterday’s most significant story about the forthcoming Brexit negotiations came not in the British Sunday newspapers, but in Welt am Sonntag.
While our own newspapers made a lot of intimations that Theresa May’s much-anticipated speech on the matter tomorrow will make it clear she is prepared for the UK to leave both the European Single Market and the Brussels-negotiated Customs Union, that German paper had a remarkable on-the-record interview with the Chancellor Philip Hammond.
Hammond had been seen in Germany —and across the Continent — as their biggest ally in the Cabinet against what those bitterly opposed to the UK’s departure from the EU invariably call ‘Hard Brexit’.
Even after the referendum result, Mr Hammond continued to issue gloomy statements about what would ensue (he had been a Remainer) — so much so that one Cabinet minister snapped: ‘It’s as though George Osborne had never left.’
But in his interview for Welt am Sonntag, Mr Hammond dashed the hopes of those who saw the Treasury as a drag anchor against what might be called the Full Brexit. He insisted the leaders of the EU ‘need to respect the British people’s sense that our history and destiny is an engagement with the rest of the world . . . historically we have never been a nation that was focused on continental Europe’.
Threat
And he issued a direct threat of what Britain would do if the EU attempted to restrict in any way our ‘access to the European market’. He declared that rather than ‘lie down and say, too bad, we’ve been wounded — if we are forced to be something different, then we will have to become something different’.
He went on to warn that Germany will pay a high price if that happened: ‘I think Mercedes-Benz and BMW and Volkswagen would also like to sell their cars in the UK market without tariffs. Germany’s biggest bank has a large operation in London and I assume it would like to continue that operation.’
I’m told the Welt am Sonntag journalists were so surprised by the tone of these remarks that they called the Treasury afterwards to check that the Chancellor really wanted to say all this on the record. The response was: Yes, he does.
It has gone off like a bomb in Berlin. The head of the Bundestag’s foreign affairs committee, Norbert Roettgen, accused our Chancellor of ‘making threats damaging the UK itself’. But then he added: ‘We should focus on common interests and compromises.’ Which actually makes a pleasant change from what we have been hearing so far from such sources, consisting entirely of warnings that Britain can expect only pain.
The interesting question is, why has Mr Hammond suddenly changed his tone from warning the British, to warning the Germans? In part, I am sure, it is because the Treasury’s predictions of what would happen to the British economy — simply as a result of voting for Brexit — have been proved scaremongering nonsense.
But it is also, in part, a negotiating tactic. The main reason David Cameron got such a pathetic deal in his so-called ‘renegotiation of our EU membership’ was that he was never prepared to walk away from the table. And Brussels knew it.
It’s not enough for Theresa May to say that if she doesn’t get a bespoke UK/EU free trade deal outside the Single Market and the Customs Union, she will walk away and risk the imposition of tariffs on both sides. She has to mean it — and be believed.
Anathema
Such rough talk from her supposedly ultra-cautious Chancellor gives her much greater credibility in such a stand-off.
But Mr Hammond’s change of tone is not just a negotiating ploy. As he also pointed out to his German interviewers: ‘Since the referendum, we have seen, on the European side, movement away from the UK positions . . . to things that are anathema to the UK: more political integration.’
Some of that ‘movement’ would now be causing political mayhem in the UK, if we had not already voted to leave. Here are just four examples.
Last week, details leaked of an EU White Paper suggesting Brussels be allowed to impose taxes directly on member states, to include a levy on CO2 emissions, an electricity tax and an EU-wide corporate income tax.
Last month, the European Court of Justice ruled that British laws allowing the security services retention of bulk data on calls and emails would not be allowed to stand as they ‘exceeded what is strictly necessary’.
Also last month, Brussels ruled that all members of the Single Market had to impose a requirement that every off-road vehicle — every quadbike, every golf-cart — had to be covered by insurance for ‘third-party injury and damage’. Our own Department for Transport said that it ‘opposed measures which impose an unreasonable burden on the public’ but that it would have to abide by the new rule until Britain exits the EU.
And, only a few days ago, Brussels ruled that even motorists who break the law by driving without insurance should be protected if their car is damaged — so law-abiding drivers face an increase in insurance bills to cover that cost.
Hostility
It is only because we are leaving the EU that these four power-grabs — proposing new EU-wide taxes; adversely affecting MI5’s ability to protect the British people; creating a totally new overhead for farmers and families playing around with quadbikes; and driving up the costs of running a car — have not caused an even sharper spike in the British people’s hostility to our membership.
Yesterday, the former Deputy PM, Nick Clegg, pleaded that Mrs May should go for a ‘Norway model’ — that is, Britain outside the EU, but still members of its Single Market. This is the same Nick Clegg who, before the referendum vote, mocked this ‘solution’: ‘Norway have to pay into EU coffers, they have to obey all EU laws: it all gets decided by everyone else in Brussels and they have to translate it into law in Oslo. They have no power whatever, all the rules get made by foreigners: utter powerlessness.’
So the most eminent representative in Westminster of the die-hard Remainers thinks such ‘powerlessness’ is better than leaving the Single Market — and, as Mrs May put it in her Conservative Party conference speech, getting ‘an agreement between an independent, sovereign United Kingdom and the European Union’.
Sorry, Mr ex-Deputy Prime Minister: you’ve lost the argument, first with the British people and, now, with the Tories who were once on your side.
Living longer? No sweat!
For years, I have had a weekly telling-off from a fine woman called Wendy. Ferociously fit and steel-muscled, every Tuesday morning she stands over me barking commands like a regimental sergeant-major, while I do the exercises she prescribes.
Each week, she asks me what exercises I’ve done since last time, and each week I tell her: ‘None whatsoever.’ Wendy then rebukes me for not doing the right thing by my own health . . . and I have no answer (anyway, I’m panting too much to make sense).
But now I have a newspaper cutting to wave at her, while I gasp and groan. Last week, the Mail reported on a research study of 64,000 British adults over a decade, which showed that just a once-weekly exercise was much more effective than had been supposed as a means of sharply reducing the chance of a premature death from heart disease.
Better still, the researchers stated that this reduction in mortality risk was no less than that experienced by people who exercised every day: ‘Those who exercised once or twice a week but did not meet the recommended levels gained similar health benefits.’
What a relief to be vindicated in my laziness. I feel better already.
Quailing at the charge that it is perpetuating ‘blackface’ — when a white actor puts on make-up to play the part of a black man — Sky Arts has pulled from the schedules its satirical drama in which Joseph Fiennes played the part of Michael Jackson.
It was the late pop-star’s daughter, Paris, protesting that she was ‘incredibly offended’ by the portrayal, which seemed to settle the matter. But would Michael Jackson himself have been offended? He had spent part of his fortune on cosmetic procedures which lightened his skin to appear more, well, like a white man.
I suspect he would have been content to be played by Fiennes. But who knows? He was very strange.
The former Tory Party leader Michael Howard has been roundly criticised for suggesting that Theresa May should be prepared to go to war to protect Gibraltar, as Margaret Thatcher did to defend the Falkland Islands after they had been invaded by Argentina.
He has been lambasted by normally sensible people for supposedly being bellicose and insulting an ally. 
The Spanish Foreign Minister, Alfonso Dastis, sniffed loftily that Britain had ‘lost composure’.
Maybe Lord Howard could have chosen his words more carefully. He was interviewed at home, and was perhaps unguarded. 
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But he was absolutely right to stress how high the stakes have become since Spain insisted it should have a veto over any final post-Brexit deal applying to Gibraltar. 
There are two crucial facts which anyone discussing the future of the British territory should bear in mind. 
One is that the Spanish authorities are absolutely obsessed with it. Gibraltar may be a small place, but gaining control of it is high in their priorities.
The second inescapable truth is that the Foreign Office and many British politicians would be happy to hand Gibraltar over to the Spanish. 
Indeed, in 2002 the Blair government cooked up a plan for joint sovereignty that was only scuppered because it was rejected in a referendum by 99 per cent of Gibraltarians in an 88 per cent turnout.
Let me give some examples of Spain’s fixation with the Rock, which seems sometimes to border on psychosis. 
It was, of course, legally ceded by Spain to Britain in 1713, and became a vital military and naval base for the British Empire.
In 1954, the fascist dictator General Franco revived Spain’s long-dormant claim to the territory after the Queen visited her loyal subjects there. 
She has not visited Gibraltar since because successive British governments have not wished to upset the prickly Spanish.
More than 99 per cent of Gibraltarians voted in 1967 against Spanish sovereignty. 
Naturally, this did not please the undemocratic, nationalist Franco, and the land border with Spain was effectively closed from 1969 to 1982.
Even with Franco’s death and the dawn of a democratic era in Spain, politicians in Madrid did not stop coveting the Rock. 
Queues periodically built up on the border as Spanish customs officials made people’s lives a misery by obstructing them as they tried to pass in and out of the territory — most recently in 2013.
Whenever British warships dock in Gibraltar, Spanish ministers are liable to be thrown into a tizz. 
There was uproar when Charles and Diana boarded the Royal Yacht Britannia off the Rock on their honeymoon in 1981. 
When he heard of their plans in advance, King Juan Carlos I of Spain boycotted their wedding.
So when Alfonso Dastis accuses the British of having ‘lost composure’, I’m afraid I have to pinch myself in disbelief. 
For years the Spanish have been anything but composed. They have been peevish, petty and sometimes bullying.
Speaking personally, if there were a tiny Spanish enclave on the coast of Cornwall, where one could pop over for a tapas and a glass of rioja, I should be delighted. 
But the macho political class in Madrid regard the very existence of Gibraltar as an affront to their honour.
They are also guilty of gross hypocrisy since the same politicians who react hysterically to the British presence in Gibraltar passionately defend Spain’s possession of Ceuta and Melilla, two enclaves in Morocco, whose government believes should be Moroccan.
The latest manifestation of Spain’s inability to accept that 99 per cent of the population of Gibraltar regard themselves as British, not Spanish, is its demand to have a say in the territory’s post-Brexit future. 
This is shameless opportunism, and it is disgraceful that the EU should have allowed it.
It can’t be stated too loudly that all 30,000 Gibraltarians are legally British, and it is the responsibility of the British Government — not Madrid or Brussels — to safeguard their rights after we have left the European Union.
The final piece of evidence that illustrates just how unbalanced the Spanish government has become was illustrated this week by a photograph of a minuscule British patrol boat (all we dare keep in Gibraltar these days) escorting a large Spanish warship out of the enclave’s territorial waters.
Such illegal incursions are frequent. This one was deliberately provocative, timed to take place days after the announcement of Spain’s diplomatic coup in obtaining from Brussels a role in discussions about the territory’s future.
Isn’t it obvious that Madrid is deadly serious — as well as pretty loopy — on this matter? 
I don’t suggest it has any intention of invading Gibraltar. As a democratically elected government, which is moreover a fellow member of the Nato military alliance, it can presumably be expected not to overturn the rule of law. 
But short of armed force, the Spanish government will try almost anything to achieve its ends. 
The trouble is that its preoccupation with Gibraltar is neither reasonable nor measured. 
So it might do something drastic. The more weakness we show, the greater the danger.
Here, I fear, we are vulnerable. For the Spanish may have seen the extreme criticisms of Lord Howard’s intervention as evidence that the British are prepared to be flexible where the future of Gibraltar is concerned.
After all, we have been so in the past, bending over backwards in order not to offend Madrid. 
In 2002, the Labour government accepted the principle of joint sovereignty with the Spanish. 
In the mind of the Foreign Office, this was doubtless one step away from handing over the Rock entirely.
Although the then foreign secretary, Jack Straw, had intimated there would be a vote on the issue, the British government wanted to present the people with a fait accompli. 
The Gibraltar government wisely decided to go ahead with a referendum of its own. The result was overwhelming. 
I’m sure Theresa May and even Foreign Secretary Boris Johnson are being genuine when they say they will respect the right of the people of Gibraltar to remain British so long as they want to — which is self-evidently for as far as anyone can see.
But there are plenty of people in Whitehall and Labour, and even some Tories, who secretly believe the enclave is an embarrassing anachronism, and the sooner it is returned to Spain the better.
The pusillanimous Foreign Office had similar thoughts about the Falklands in 1981. 
The watering down of British citizenship rights for their inhabitants, as well as the withdrawal of a major supply vessel, persuaded the Argentines that we were no longer committed to defending the islands. 
However, treacherous mandarins had not counted on Margaret Thatcher’s conviction and courage.
We can easily imagine what such people will say when Spain threatens to unpick a Brexit deal unless it can obtain concessions over Gibraltar. 
They will bleat that 30,000 people can’t be allowed to stand in the way of an agreement.
So despite his somewhat clumsy language, I’m on Lord Howard’s side. He realises the enormity of the danger facing our fellow British citizens. 
Never forget: Spain craves Gibraltar, and will move heaven and earth to get it.
The issue could come to a head as soon as today with leading Brexiteers branding the Treasury 'Brexit saboteurs'
PHILIP Hammond is blocking calls to increase spending on No Deal planning at this month’s Budget - as hopes of a Brussels breakthrough grow.
The Chancellor has been urged by some in Government to set aside even more funds to prepare for a collapse in negotiations, beyond the £3 billion he earmarked in 2017.
But Treasury insiders say he is resisting any increase, even if it strengthened Theresa May’s negotiating hand and is likely the cash will never have to be spent.
The issue could come to a head as soon as today as the Cabinet discuss the Budget.
One Cabinet Minister told The Sun “it seems like a no-brainer” as Brexit talks go to the wire, as it would send the message to Brussels that Britain really is ready to walk away.
And a senior Government source added they “definitely need” more cash to prepare for the doomsday scenario of Britain exiting the EU without a trade deal in place next March.
But Treasury sources insisted there was already enough funding for emergency planning scenarios.
Last night leading Brexiteer Iain Duncan Smith publicly backed calls for more money, saying: “How can the PM say we are preparing to leave the EU without a deal when her Chancellor is refusing to pay for it?”
And in an extraordinary blast, the former Tory leader added: “If the money isn’t forthcoming the it means the Treasury is acting like government saboteurs - hell bent on wrecking Brexit.”
The spat comes as the business chiefs urged Mr Hammond to use his fiscal statement in two weeks time to radically prepare the country for exit with a £3 billion package.
The CBI’s plans include more than doubling the tax breaks export firms get to invest in their own factories to £500,000 and doubling apprenticeship investment to get Britain Brexit ready.
They also suggest a business rates holiday for any firm that conducts a major overhaul of their store, factory or office.
Boss Carolyn Fairburn said: “As the UK leaves the EU, there is no better moment than this Budget to show the Government is committed to real partnership with business.”
The issue could come to a head as soon as today with leading Brexiteers branding the Treasury 'Brexit saboteurs'
PHILIP Hammond is blocking calls to increase spending on No Deal planning at this month’s Budget - as hopes of a Brussels breakthrough grow.
The Chancellor has been urged by some in Government to set aside even more funds to prepare for a collapse in negotiations, beyond the £3 billion he earmarked in 2017.
But Treasury insiders say he is resisting any increase, even if it strengthened Theresa May’s negotiating hand and is likely the cash will never have to be spent.
The issue could come to a head as soon as today as the Cabinet discuss the Budget.
One Cabinet Minister told The Sun “it seems like a no-brainer” as Brexit talks go to the wire, as it would send the message to Brussels that Britain really is ready to walk away.
And a senior Government source added they “definitely need” more cash to prepare for the doomsday scenario of Britain exiting the EU without a trade deal in place next March.
But Treasury sources insisted there was already enough funding for emergency planning scenarios.
Last night leading Brexiteer Iain Duncan Smith publicly backed calls for more money, saying: “How can the PM say we are preparing to leave the EU without a deal when her Chancellor is refusing to pay for it?”
And in an extraordinary blast, the former Tory leader added: “If the money isn’t forthcoming the it means the Treasury is acting like government saboteurs - hell bent on wrecking Brexit.”
The spat comes as the business chiefs urged Mr Hammond to use his fiscal statement in two weeks time to radically prepare the country for exit with a £3 billion package.
The CBI’s plans include more than doubling the tax breaks export firms get to invest in their own factories to £500,000 and doubling apprenticeship investment to get Britain Brexit ready.
They also suggest a business rates holiday for any firm that conducts a major overhaul of their store, factory or office.
Boss Carolyn Fairburn said: “As the UK leaves the EU, there is no better moment than this Budget to show the Government is committed to real partnership with business.”
Lawyers urged the gypsy community to ensure they gather the right paperwork as soon as possible
GYPSIES and travellers have been warned they could be deported after Brexit if they don't have proof they can stay.
Lawyers have urged the community to get their paperwork in order as soon as possible - or risk being thrown out of the country.
The situation could end up seeing travellers forced to leave the UK because they don't have the right documents, in an echo of the Windrush generation scandal.
The Traveller Movement national annual conference heard that gypsies may have difficulty gathering official paperwork to prove they have the right to live here.
Poor literacy, the inability to use computers, the cost of applying and distrust of the state were all cited as barriers to claiming the "settled status" which non-citizens need to have in order to stay in Britain after Brexit.
Lawyer Christopher Desira said travellers should start gathering paperwork such as tax documents, education certificates, bank statements or employment contracts.
He warned that they could end up confined in a detention centre, particularly if they don't have a passport.
Charity worker Sarah Zawacki added: "Our work found that there was also a very low awareness of the need to apply to secure their position in the UK.
"Now they know there is this application, but it's £65 - many are on very low incomes and have very large families and it's just unfeasible.
"Then there is the language barrier - many speak some English but it's not the level needed to access this application."
Around 300,000 members of the Roma community are believed to live in the UK.
Some were born and brought up in the country, but others moved here from other parts of the EU.
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Lawyers urged the gypsy community to ensure they gather the right paperwork as soon as possible
GYPSIES and travellers have been warned they could be deported after Brexit if they don't have proof they can stay.
Lawyers have urged the community to get their paperwork in order as soon as possible - or risk being thrown out of the country.
The situation could end up seeing travellers forced to leave the UK because they don't have the right documents, in an echo of the Windrush generation scandal.
The Traveller Movement national annual conference heard that gypsies may have difficulty gathering official paperwork to prove they have the right to live here.
Poor literacy, the inability to use computers, the cost of applying and distrust of the state were all cited as barriers to claiming the "settled status" which non-citizens need to have in order to stay in Britain after Brexit.
Lawyer Christopher Desira said travellers should start gathering paperwork such as tax documents, education certificates, bank statements or employment contracts.
He warned that they could end up confined in a detention centre, particularly if they don't have a passport.
Charity worker Sarah Zawacki added: "Our work found that there was also a very low awareness of the need to apply to secure their position in the UK.
"Now they know there is this application, but it's £65 - many are on very low incomes and have very large families and it's just unfeasible.
"Then there is the language barrier - many speak some English but it's not the level needed to access this application."
Around 300,000 members of the Roma community are believed to live in the UK.
Some were born and brought up in the country, but others moved here from other parts of the EU.
We pay for your stories! Do you have a story for The Sun Online politics team? Email us at tips@the-sun.co.uk or call 0207 782 4368. We pay for videos too. Click here to upload yours
Brexiteers fear that soon they’ll either have to take the blame for a no-deal Brexit or be bounced into backing a flawed deal — and Theresa May’s 'astonishingly upbeat' mood is a signal
IT is quiet out there, too quiet in the views of many Brexiteers in government.
Their suspicions are raised by the fact that when things go silent in Brussels, that’s when the real negotiating is being done. They fear that right now a deal is being done that they’ll be bounced into supporting.
They worry that since last week’s Cabinet meeting, there hasn’t been any new Brexit offer put either to Cabinet or the inner cabinet, yet technical talks have resumed in Brussels.
They fear that a deal will be agreed. Then, they’ll be faced with a choice of rejecting it and having to take the blame for no deal and the chaos that would involve or accepting the agreement with all its flaws.
This fear of being bounced has been heightened by Theresa May’s mood. Those who have seen her this week describe her as “astonishingly upbeat” and convinced that a deal will soon be done.
I understand that she will update the Cabinet on the state of negotiations on Tuesday.
Dominic Raab, the Brexit Secretary, is more optimistic than most Leavers in Cabinet. He has been reassuring Cabinet colleagues that press reports about where the deal is going to end up aren’t right and that the final phase of the negotiations will be politically — not technically — led. In other words ministers, not civil servants, will be in charge.
But this has not been enough to assuage some of his colleagues’ concerns.
They point out that at crucial points in these negotiations, Downing Street has presented ministers with a done deal and challenged them to quit if they don’t like it. The Chequers plan, which David Davis and Boris Johnson resigned over, was just one example of this approach.
These ministers have concluded that the level of concern the Cabinet expressed about the negotiations means that Mrs May will not come to the Cabinet and ask ministers for permission to make further concessions. Rather, they’ll simply be presented with them.
At the top level of government, they are keen to get the EU to agree to a special Brexit meeting this month.
They believe that will give them more time to get the deal through parliament. An agreement in November would also allow them to avoid some of the most difficult no-deal planning choices. For instance, I understand that at Cabinet on November 13 they must decide whether to book space on ferries to bring in essential supplies in the event of no deal.
Number 10 is confident of getting a Brexit deal through the Commons. One of those who has discussed the matter with Mrs May tells me “you can see how opposition melts away” in the face of worries about both no deal and a Corbyn government.
At the same time, the May circle believe the carrot of a future trade deal with the EU and the Government having more money to spend if the withdrawal agreement is passed will ease its passage.
But Theresa May should beware buyer’s remorse. She may well be able to bounce her Cabinet and the bulk of her MPs into supporting a deal.
But if they end up regretting their vote or are left angry, they’ll know who to blame. Mrs May will find herself facing a confidence vote next spring.
“A MASTERCLASS in how to give people something and p**s them off at the same time” – that’s how one senior Tory describes Philip Hammond telling schools that they could have £400million to buy the “little extras they need”.
Schools funding is one of the issues that cost the Tories most at the last election. But the Budget did little to deal with this question: More than 80 per cent of the extra spending announced went to the NHS and there was more new money for potholes than schools.
Education is threatening to turn into a major political problem for the Tories.
A new TV series called School, starting on Tuesday on BBC2, looks at how schools are struggling to cope with budgetary constraints. At the same time, the Tories and their anonymous Education Secretary Damian Hinds are oddly quiet about their achievements.
The free schools set up under this Government are outperforming all other schools. But the Government barely whispers about this, when it should be shouting it from the rooftops.
Downing Street defends the emphasis on the NHS to Tory MPs by pointing out that their polling shows it is the overwhelming public-spending priority of their supporters. But as one influential Tory complains to me, this ignores the fact that people now only become more likely to vote Tory than Labour at age 47.
“If you want to have some supporters who are less elderly, you might want to push education up the agenda,” he fumes.
The Tories won’t win back their majority without more support from those in their thirties and early forties – and they won’t win over parents with school-age children unless they show them that education is as much of a priority for the Government as it is for them.

THE view in Westminster is that Monday was Philip Hammond’s last Budget. There are whispers in Whitehall that his travel schedule and raised international profile suggest he realises as much.
So, who will replace Hammond as Chancellor? Well, the rumour in government circles is that Amber Rudd, cleared now of blame for the Windrush scandal, might. She is a former banker who knows the Treasury well and would be the first female Chancellor.
Mrs Rudd would, from No10’s point of view, also be less of a threat than other contenders. Her small majority in Hastings and her position on Brexit make her less of a challenge to Mrs May’s position.

JEREMY Hunt is determined to banish the idea that Brits can only speak two languages: English and English slower and louder.
After giving a speech in Japanese in September, he is giving one entirely in French on Thursday.
Let’s hope that Mr Hunt fares better than Tory Blair. When he gave a speech in French to their parliament, there were complaints that his accent owed too much to his time as a barman in Paris.

AN incompetent minister in a competent department can be dealt with.
A hyper-competent minister can stop an incompetent department making too many mistakes.
But put together an incompetent department and an incompetent minister and you have a guaranteed disaster on your hands.
But that is what we have with immigration right now. Caroline Nokes, the Immigration Minister, is one of the weakest members of the Government, while the Home Office is still not fit for purpose ­– as the Windrush scandal showed.
What makes all this so dangerous is that Brexit will have huge consequences for immigration policy.
THIS week has shown why the Tories should be more afraid of John McDonnell than Jeremy Corbyn.
It was Mr McDonnell who realised that Labour would be walking into an elephant trap if they opposed plans to raise the higher rate tax threshold to £50,000.
Mr McDonnell knows that if Labour is to win next time, they’ve got to make people think that only “the rich” and big business will end up paying more tax.

Brexiteers fear that soon they’ll either have to take the blame for a no-deal Brexit or be bounced into backing a flawed deal — and Theresa May’s 'astonishingly upbeat' mood is a signal
IT is quiet out there, too quiet in the views of many Brexiteers in government.
Their suspicions are raised by the fact that when things go silent in Brussels, that’s when the real negotiating is being done. They fear that right now a deal is being done that they’ll be bounced into supporting.
They worry that since last week’s Cabinet meeting, there hasn’t been any new Brexit offer put either to Cabinet or the inner cabinet, yet technical talks have resumed in Brussels.
They fear that a deal will be agreed. Then, they’ll be faced with a choice of rejecting it and having to take the blame for no deal and the chaos that would involve or accepting the agreement with all its flaws.
This fear of being bounced has been heightened by Theresa May’s mood. Those who have seen her this week describe her as “astonishingly upbeat” and convinced that a deal will soon be done.
I understand that she will update the Cabinet on the state of negotiations on Tuesday.
Dominic Raab, the Brexit Secretary, is more optimistic than most Leavers in Cabinet. He has been reassuring Cabinet colleagues that press reports about where the deal is going to end up aren’t right and that the final phase of the negotiations will be politically — not technically — led. In other words ministers, not civil servants, will be in charge.
But this has not been enough to assuage some of his colleagues’ concerns.
They point out that at crucial points in these negotiations, Downing Street has presented ministers with a done deal and challenged them to quit if they don’t like it. The Chequers plan, which David Davis and Boris Johnson resigned over, was just one example of this approach.
These ministers have concluded that the level of concern the Cabinet expressed about the negotiations means that Mrs May will not come to the Cabinet and ask ministers for permission to make further concessions. Rather, they’ll simply be presented with them.
At the top level of government, they are keen to get the EU to agree to a special Brexit meeting this month.
They believe that will give them more time to get the deal through parliament. An agreement in November would also allow them to avoid some of the most difficult no-deal planning choices. For instance, I understand that at Cabinet on November 13 they must decide whether to book space on ferries to bring in essential supplies in the event of no deal.
Number 10 is confident of getting a Brexit deal through the Commons. One of those who has discussed the matter with Mrs May tells me “you can see how opposition melts away” in the face of worries about both no deal and a Corbyn government.
At the same time, the May circle believe the carrot of a future trade deal with the EU and the Government having more money to spend if the withdrawal agreement is passed will ease its passage.
But Theresa May should beware buyer’s remorse. She may well be able to bounce her Cabinet and the bulk of her MPs into supporting a deal.
But if they end up regretting their vote or are left angry, they’ll know who to blame. Mrs May will find herself facing a confidence vote next spring.
“A MASTERCLASS in how to give people something and p**s them off at the same time” – that’s how one senior Tory describes Philip Hammond telling schools that they could have £400million to buy the “little extras they need”.
Schools funding is one of the issues that cost the Tories most at the last election. But the Budget did little to deal with this question: More than 80 per cent of the extra spending announced went to the NHS and there was more new money for potholes than schools.
Education is threatening to turn into a major political problem for the Tories.
A new TV series called School, starting on Tuesday on BBC2, looks at how schools are struggling to cope with budgetary constraints. At the same time, the Tories and their anonymous Education Secretary Damian Hinds are oddly quiet about their achievements.
The free schools set up under this Government are outperforming all other schools. But the Government barely whispers about this, when it should be shouting it from the rooftops.
Downing Street defends the emphasis on the NHS to Tory MPs by pointing out that their polling shows it is the overwhelming public-spending priority of their supporters. But as one influential Tory complains to me, this ignores the fact that people now only become more likely to vote Tory than Labour at age 47.
“If you want to have some supporters who are less elderly, you might want to push education up the agenda,” he fumes.
The Tories won’t win back their majority without more support from those in their thirties and early forties – and they won’t win over parents with school-age children unless they show them that education is as much of a priority for the Government as it is for them.

THE view in Westminster is that Monday was Philip Hammond’s last Budget. There are whispers in Whitehall that his travel schedule and raised international profile suggest he realises as much.
So, who will replace Hammond as Chancellor? Well, the rumour in government circles is that Amber Rudd, cleared now of blame for the Windrush scandal, might. She is a former banker who knows the Treasury well and would be the first female Chancellor.
Mrs Rudd would, from No10’s point of view, also be less of a threat than other contenders. Her small majority in Hastings and her position on Brexit make her less of a challenge to Mrs May’s position.

JEREMY Hunt is determined to banish the idea that Brits can only speak two languages: English and English slower and louder.
After giving a speech in Japanese in September, he is giving one entirely in French on Thursday.
Let’s hope that Mr Hunt fares better than Tory Blair. When he gave a speech in French to their parliament, there were complaints that his accent owed too much to his time as a barman in Paris.

AN incompetent minister in a competent department can be dealt with.
A hyper-competent minister can stop an incompetent department making too many mistakes.
But put together an incompetent department and an incompetent minister and you have a guaranteed disaster on your hands.
But that is what we have with immigration right now. Caroline Nokes, the Immigration Minister, is one of the weakest members of the Government, while the Home Office is still not fit for purpose ­– as the Windrush scandal showed.
What makes all this so dangerous is that Brexit will have huge consequences for immigration policy.
THIS week has shown why the Tories should be more afraid of John McDonnell than Jeremy Corbyn.
It was Mr McDonnell who realised that Labour would be walking into an elephant trap if they opposed plans to raise the higher rate tax threshold to £50,000.
Mr McDonnell knows that if Labour is to win next time, they’ve got to make people think that only “the rich” and big business will end up paying more tax.

Last modified on Tue 8 Jan 2019 11.51 GMT
Moves to ask parents to submit the country of birth of their children this week as part of the school census have caused a significant backlash on social media, with parents being urged to boycott the survey via the #BoycottSchoolCensus hashtag campaign. Here are the answers to some of the key questions about the census and the campaign against it.
State schools in England supply details about their pupils to the Department for Education for what is known as the school census once every term. The census includes details such as age, address and academic attainments, and these are recorded in the national pupil database (NPD). National statistics from the survey are published every year. Here’s the 2016 edition.
Last year, long before the EU referendum, the DfE decided to add new components for the 2016-17 census, including pupils’ country of birth and nationality. It also started to ask schools to judge children’s proficiency in English if it is not their first language. The DfE has collected data on pupils’ ethnicity for many years.
No. There are reports that many schools have reacted to the new questions on birth and nationality by asking to do so, but the DfE says parents are not obliged to comply.
Schools and local authorities are allowed to ask for proof of date of birth during the admissions process, but the DfE’s code specifically states they must not ask for “long” birth certificates or “other documents which include information about the child’s parents”.
At a basic level the DfE uses the school census for funding and planning. Its intention in adding nationality and language ability was to help gauge the “targeting of support” for pupils and schools. Academics and journalists conducting research also make extensive use of the database. Figures showing that grammar schools have a tiny number of pupils on free school meals, for example, are likely to have come via the NPD.
Access to the NPD is restricted, and the restrictions increase with the level of detail. The highest level of access – known as tier one and which could identify individual pupils – is only open to a small number of approved applicants, and details identifying individual pupils cannot be divulged.
Condition of access includes compliance with the Data Protection Act 1998. This means providing proof of registration with the information commissioner’s office, having appropriate security arrangements in place to process the data, using the data only for the specific purpose requested, keeping it only for the specified length of time and not sharing it without prior written approval.
Update: the highest level of access to data is tier one, not tier four as previously stated.
Some people fear the Home Office could use the database to identify foreign-born families, or match the findings to its own immigration database. The timing of the census has heightened this worry.
The change was suggested a year ago, but the subsequent vote in favour of leaving the European Union has left the immigration status of EU nationals living in the UK much less clear than it was 12 months ago. With Liam Fox suggesting that they could be “one of our main cards in the negotiations” for Brexit, and the home secretary, Amber Rudd, suggesting companies could be forced to reveal how many foreign workers they have, the political atmosphere is highly charged.
Campaigners say the Home Office has a record of accessing other government departments’ data, but the DfE’s official line is that the information will not be shared: “These data items will not be passed to the Home Office. They are solely for internal DfE use for analysis, statistics and research,” it said.
It is worth noting that the Home Office could already do something similar through existing HMRC tax records.
Yes, to a point. The DfE’s guidance to schools allows parents and carers to refuse to supply the information on nationality and place of birth. It is the first time parents have been given that right in the school census. The school will still supply all the other data it already collects on pupils.
It’s very much a matter of personal conscience.
It is unlikely the Home Office is trawling the NPD looking for immigrants. It doesn’t currently have the capacity, though it could perhaps in the future. Many school leaders are in favour of the data collection, because it helps them argue for further funding for new places and additional support for those needing to learn English.
Boycotting the data collection would send a strong signal to the DfE that they are being too intrusive in their methodology, and that parents are concerned about the potential abuse of the data in the future. One thing is clear though: no schools should be badgering parents to see passports, and parents are entirely right to be refusing these requests.
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From The Socialist newspaper, 28 September 2016
TUSC parliamentary candidates in 2015, photo Senan   (Click to enlarge)
Jeremy Corbyn's re-election triumph is a significant defeat for the capitalist establishment - the corporate bosses, media tops, and their political representatives, both those outside and inside the Labour Party. Prior to Jeremy's election as leader last summer this elite had achieved unchallenged control of the Labour Party for over 20 years, effectively disenfranchising working class voters by removing any choice at the ballot box.
The capitalists benefitted enormously from the transformation of Labour into Tony Blair's New Labour and they will not lightly accept the new situation. Consolidating Jeremy's victory against their continued opposition - by really transforming Labour into an anti-austerity, socialist, working-class mass movement - is the critical task facing socialists in Britain today.
The first meeting of the Trade Unionist and Socialist Coalition (TUSC) national steering committee after Jeremy Corbyn's re-election takes place on 12 October. The Socialist Party will be presenting proposals on how TUSC can contribute to the central task at hand.
TUSC was established in early 2010 and initially involved the Socialist Party and a number of leading trade unionists participating in a personal capacity.
These included Bob Crow, the general secretary of the 80,000-strong RMT transport workers' union, which had been expelled from the Labour Party in 2004. The RMT's predecessor union was one of the founding organisations of the Labour Party.
In 2012 the RMT's annual delegate general meeting (AGM) agreed that the union would formally participate as a constituent organisation of TUSC, with representatives appointed to the coalition's steering committee. The RMT's continued involvement has been endorsed, not without debate, at every AGM since.
The Socialist Workers' Party was invited into TUSC in 2010 and independent socialists also participate. By providing a common electoral umbrella for trade unionists and working class community campaigners to challenge establishment politicians at the ballot box in defence of core socialist policies, TUSC's aim has been to push forward the process of re-establishing a vehicle for working class political representation.
The TUSC founding statement recognised that there were "different strategic views" about the way to advance this cause, "whether the Labour Party can be reclaimed by the labour movement, or whether a new workers' party needs to be established." But aside from recognising that there would be Labour candidates "who share our socialist aspirations" who would not be challenged by TUSC, to date TUSC has not taken a policy position on what would be required to transform the Labour Party. Jeremy Corbyn's re-election poses this question point blank.
The Socialist Party is proposing that TUSC makes a clear policy statement that a critical step would be to re-establish within the Labour Party a role for trade unions, the biggest voluntary organisations in Britain, commensurate with their importance as the collective voices of millions of workers.
Under Blair, Brown and Miliband the unions' power within the Labour Party was gutted. The real social weight of the RMT, for example, is shown when it is routinely denounced by the capitalist media as 'holding the country to ransom' every time it is forced to take strike action to defend its members and public safety on the railways.
But if the union was to affiliate to the Labour Party today it would have less say than the House of Lords Labour Group in the party's national policy-making forum! As the RMT's political strategy endorsed by this year's AGM says, Labour does not currently have "structural/constitutional arrangements that would make affiliation in the union's interests."
The Socialist Party is not proposing that TUSC draws up an alternative constitution for the Labour Party. TUSC is a coalition whose component parts have different views. But it could agree a broad policy to take into the labour movement: that the unions must have their collective representation and proportionate weight restored in the formation of Labour Party policy, the selection and re-selection of Labour Party candidates, and the administration of the party locally and nationally.
The RMT rulebook commits the union "to work for the supersession of the capitalist system by a socialistic order of society." There should be no problem for TUSC to also adopt policy that socialists excluded from the Labour Party should be allowed in.
The best way to achieve this - above board and undercutting media scares about 'infiltrators' - would be to allow for affiliation to the Labour Party for socialist parties and organisations. This right should also be extended to anti-austerity, anti-racist, socialist feminist, and Green campaigners and organisations, in a modern version of the early federal structure of the Labour Party which encompassed trade unions, the co-operative movement, women's suffrage campaigners, and a number of independent socialist parties.
But this call obviously raises the question of TUSC's electoral activity.
The Co-operative Party, an independent party separately registered with the Electoral Commission, has an affiliate status agreement with the Labour Party on the basis that it does not contest seats against Labour. The Socialist Party will be proposing at the October steering committee that TUSC should campaign for a similar arrangement for its constituent components.
Since Jeremy Corbyn's initial victory, TUSC has already re-calibrated its electoral activity.
In the May 2016 local elections, for example, no TUSC candidates were even considered to be run without local TUSC groups seeking a dialogue with the sitting Labour councillor or prospective candidate on the critical issue of their preparedness to resist cuts to local council jobs and services (see www.tusc.org.uk/txt/380.pdf for a full report of TUSC's participation in the 2016 elections).
The Socialist Party is proposing that TUSC continues its campaign for Labour councils to join the resistance to the Tories' austerity agenda. TUSC supporters have played an important role in winning backing for a fighting strategy to oppose cuts to local public services in the main local government unions, Unison, Unite, and the GMB, as well as this year's Wales TUC conference.
This campaign should be resumed in the autumn, as councils begin preparing their 2017-18 budgets, with the added urgency of the need to coordinate an organised defiance of the new Housing and Planning Act. Labour councillors should be pushed to fight the Tories or resign and make way for those who will.
However the responsibility for removing alleged 'Labour' representatives who implement Tory policies does not rest with TUSC alone. TUSC candidates have polled over 350,000 votes in various elections since its formation and the prospect of an electoral challenge from the left can add to the pressure on 'Labour' cutters.
But with Jeremy Corbyn's re-affirmed mandate it is not the only way to bring them into line. The councillors on the Labour-controlled Greater Manchester Fire and Rescue Service Authority, for example, who are planning to sack one in five firefighters and re-employ the rest on worse contracts, should be suspended from the Labour Party unless they back down.
Consequently, the Socialist Party is proposing that TUSC agrees to make no further preparations for contesting the May 2017 local elections in England and Wales pending discussions with Jeremy Corbyn and his supporters on the new possibilities opening up following his re-election victory.
Many other organisational and political steps would need to be taken for the Labour Party to be fully consolidated as a working class, socialist, anti-austerity mass movement. This would include measures to defeat the opposition that will continue to Jeremy Corbyn's leadership from Labour's right.
TUSC's constituent components will have different views on how best a movement can be built that is capable of defeating the pro-capitalist consensus upheld by the establishment politicians, their media, and other institutions.
But October's steering committee discussion, in welcoming Jeremy Corbyn's re-election triumph, provides an opportunity to signal that TUSC will fully participate in that struggle.
The coronavirus crisis has laid bare the class character of society in numerous ways. It is making clear to many that it is the working class that keeps society running, not the CEOs of major corporations.
The results of austerity have been graphically demonstrated as public services strain to cope with the crisis.

Amnesty to conduct research into racism in the UK
‘Some people now feel licensed to express racist views in a way we haven’t seen for decades’ – Kate Allen
Amnesty International today announced a new emergency campaign to combat racism and xenophobia in the UK, prompted by reports of a rise in racial abuse in the wake of the EU referendum.
The announcement comes amid news that reports to police of online hate crimes rose over the weekend since Thursday’s referendum. The UN has also raised concern over the reported rise.
Amnesty will conduct research into the rise in racism and xenophobia across the UK. The new research will examine reports of abuse and their causes, including the public and political discourse around both the EU referendum and the London mayoral election.
Amnesty has issued an urgent call on all local councils to condemn racism in all its forms, and to commit to ensuring that all local bodies and programmes have the support and resources needed to fight and prevent racism and xenophobia. Amnesty aims to get every local council to sign up to the commitment. (www.amnesty.org.uk/againsthate)
Meanwhile Amnesty is encouraging people to show their solidarity with people experiencing abuse, using the #AgainstHate hashtag.
Kate Allen, Amnesty’s UK Director, said:
“Some people now feel licensed to express racist views in a way we haven’t seen for decades.
“The referendum campaign was marked by divisive, xenophobic rhetoric as well as a failure from political leaders to condemn it. We are now reaping the referendum rhetoric whirlwind.
“Amnesty is deeply concerned at reports of verbal abuse, attacks on buildings, racist slogans on t-shirts, calls for people to leave the country and other acts of intimidation and hate.
“People across the UK have suddenly found themselves in a country where they’re unsure of their future, their family’s future and the security of their jobs and homes. They need to be urgently reassured that they can feel safe, protected and welcome here.
“We’re simply not prepared to stand by and let hate become the norm in Britain.”
A member of Amnesty’s Belfast group was verbally racially abused on Saturday night by a man who asked him if he was from the European Union before telling him to “get the fuck out of our country”.
Mohammed Samaana, a nurse in a Belfast hospital, was verbally attacked in a city-centre Belfast bar. He describes the incident:
“On Saturday night, a man I have never met before said to me: “You from the EU? Fuck off back to your country. Get the fuck out of our country.”
“At first I thought he was joking, but then he continued the abuse and started shaking his fists at me. At that point I decided it was better to leave rather than have the incident escalate.
“What makes me really sad is that the three men and three women who were with him didn’t say a word, condoning his racism by their silence. I think everyone now needs to speak out and challenge racism wherever and whenever we see it.”
Mr Samaana is a dual Palestinian-UK citizen who has lived in Northern Ireland for fifteen years and works as a nurse in a Belfast hospital.
Today the UN High Commissioner for Human Rights Zeid Ra’ad Al Hussein issued a statement on xenophobic attacks in the United Kingdom:
“I am deeply concerned at reports of attacks and abuses targeting minority communities and foreign citizens in the United Kingdom over the last few days. Racism and xenophobia are completely, totally and utterly unacceptable in any circumstances. I urge the U.K. authorities to act to stop these xenophobic attacks and to ensure that all those suspected of racist and anti-foreigner attacks and abuses are prosecuted.”

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Prime Minister Pedro Sánchez has said Spain will reject the draft Brexit withdrawal deal without a clarification of the text on future talks on the status of Gibraltar.
Spain maintains a claim to the peninsula, ceded to the British crown under the 1713 Treaty of Utrecht.
It wants to ensure that future EU talks with the UK do not cover Gibraltar.
"As things stand today if there are no changes regarding Gibraltar, Spain will vote no on Brexit," said Mr Sánchez.
Throughout the Brexit negotiations, Spain - along with Ireland and Cyprus - has conducted separate talks with the UK about specific border issues.
On Monday Spanish Foreign Minister Josep Borrell said that the draft Brexit deal had failed to make clear that talks on Gibraltar were "separate negotiations" and not part of future talks between the UK and EU.
Mr Sánchez added his weight to those remarks on Tuesday at a forum in Madrid, emphasising that any future negotiations on Gibraltar had to be bilateral.
"As a country we cannot assume that whatever happens in the future with Gibraltar would be negotiated by the UK and EU - it will have to be negotiated between Spain and the UK," he said.
Article 184 of the draft Brexit deal says the EU and the UK will seek to "negotiate rapidly the agreements governing their future relationship" between the official day of withdrawal on 29 March 2019 and the end of a transition period in December 2020.
But Spain believes the article in question is ambiguous and wants to ensure that this does not apply to the future of Gibraltar. It insists on its future right to discuss the status of the peninsula bilaterally with the UK, and is seeking clarity that this draft deal will allow it to do so.
Asked about the Spanish objection to Article 184, a European Commission spokesman said they were aware of Spain's concerns. He said the EU's position on Gibraltar had been made clear in April 2017 guidelines, that after Brexit no agreement between the EU and UK could apply to Gibraltar without the agreement of the UK and Spain.
Gibraltar's Chief Minister Fabian Picardo accused Spain of adopting a "well-known tactic" of raising issues at the last minute. He said Spain's position "does little to build mutual confidence and trust going forward".
A spokesperson for UK Prime Minister Theresa May said the draft deal covered Gibraltar as well as "the other overseas territories and the crown dependencies".
"We will get a deal that works for the whole UK family."
By Gavin Lee, Europe reporter
Spain and Britain have been running parallel negotiations over the future of Gibraltar, alongside the main EU-UK Brexit negotiations. Those talks have led to a "protocol" being agreed and three Spanish-British committees being set up to tackle tobacco smuggling, oversee cross-border workers rights, and co-operate on environmental protection and border control.
There seemed to be no drama on the horizon and the Spanish prime minister told me a few weeks ago he had "no significant concerns over Gibraltar", that the "behaviour of the British government was good" and an agreement could be reached.
So what has changed?
The Spanish government says that its "bone of contention" is with one specific article in the draft Withdrawal Agreement that was only added last week, just before it was signed off by the European Commission, and wasn't seen by Spanish negotiators.
A senior Spanish diplomat told me that Spain wanted the following words (or similar) added to Article 184: "This does not apply to Gibraltar, which will be subject to bilateral talks between the UK and Spain."
Underlying all of this is the fact that Spain still disputes that Gibraltar as a British overseas territory. Spanish officials refer to the rock as a "British colony" and, although the Spanish government isn't seeking to use the Brexit talks to push that claim, it is making it clear that any decision over the future of Gibraltar can only happen with the approval of Madrid.
Though Spain ceded the peninsula under the 1713 treaty, it has tried several times to regain control over it.
A referendum in the territory in 1967 saw 99.6% of residents vote to remain British. A proposal for joint sovereignty was also decisively rejected by Gibraltarians in a 2002 vote.
Spain closed its border with Gibraltar after the 1967 vote and did not fully reopen it until 1985, the year before Spain joined the European Economic Community - the forerunner of the EU.
Gibraltar profile

Brexit talks have made "little" progress since March, the EU's chief negotiator has said.
Michel Barnier said there was a "risk of failure" in two key areas - Northern Ireland, and how the agreement will be governed.
He said June's EU summit was a "key rendezvous" to reach a deal that can be ratified before the UK leaves.
And he defended the EU's stance over the UK's involvement in the new Galileo sat-nav system.
The UK has played a key role in the programme's development so far, but faces being shut out of key elements of the programme after Brexit.
UK ministers are now considering setting up a rival version.
Mr Barnier said there had been "misunderstandings" in the coverage of the story, adding: "We are not kicking the UK out of Galileo. The UK decided unilaterally and autonomously to withdraw from the EU. This implies leaving its programmes as well."
EU rules mean the UK and its companies cannot participate in the "development of security sensitive matters", he said, adding that this did not mean the UK could not use an encrypted signal from the system as a third country.
Earlier Science Minister Sam Gyimah said the EU's position was "extremely disappointing".
"The EU is playing hard ball with us," he told BBC Radio 4's Today programme.
"We have helped to develop the Galileo system. We want to be part of the secure elements of the system and we want UK industry to be able to bid for contracts on a fair basis.
"It is only on those terms that it makes sense for the UK to be involved in the project."
Mr Barnier was speaking after updating the remaining EU member states on the latest in the Brexit negotiations.
Asked about the progress that had been made since March, he said: "I would say little, not very little."
He said the transition period that is expected to follow Brexit day in March 2019 depended on "operational solutions" being found on the issue of Northern Ireland's border with the Republic.
"The clock is ticking" to reach an agreement before October or November which can be ratified by the UK and European Parliaments and the EU Council, he said.
"So, little progress but we are working on technical issues which is always useful.
"None of these issues are negligible. The two key points which remain, where there is risk of failure, are the governance of the agreement and the  Ireland-Northern Ireland issue."
The UK government has yet to settle on the model it wants to replace the customs union in order to avoid checks at Northern Ireland's border with the EU.
Prime Minister Theresa May met Conservative MPs at Downing Street to set out the government's two proposals.
Earlier Health Secretary Jeremy Hunt warned Foreign Secretary Boris Johnson - who has described one, a customs partnership, as "crazy" - to keep discussions private.
"On the EU side, if they see divisions in the open, they will exploit that," Mr Hunt said.
At a press conference with his French counterpart, Mr Johnson was asked why he had not resigned given his differences with the prime minister -  but he did not repeat his criticism of the partnership option and said he thought Mrs May's position was "completely right".
Mrs May's key Brexit committee of senior ministers - which is divided over the customs issue - meets again on Tuesday.

A legal challenge to try to prevent Boris Johnson shutting down parliament to force through a no-deal Brexit has begun in a Scottish court.
A group of MPs and peers wants the Court of Session in Edinburgh to rule that suspending parliament to make the UK leave the EU without a deal is "unlawful and unconstitutional".
The prime minister has repeatedly refused to rule out such a move.
Lord Doherty agreed to hear arguments from both sides in September.
However he refused to accelerate the case through the Scottish courts, with the petitioners voicing fears that they may run out of time before the UK is due to leave the EU on 31 October.
The start of the legal action came as it emerged the UK government expects a group of MPs to try to block a no-deal Brexit by attempting to pass legislation when Parliament returns next month.
A No 10 source said they expected the challenge to come in the second week of September, when MPs are due to debate a report on Northern Ireland.
The source assumes the EU will wait until after that date before engaging in further negotiations.
More than 70 politicians have put their names behind the move, including Lib Dem leader Jo Swinson and SNP MP Joanna Cherry.
A challenge brought by the same group of anti-Brexit politicians last year saw the European Court of Justice rule the UK can cancel Brexit without the permission of the other 27 EU members.
Jolyon Maugham QC, director of the Good Law Project which is supporting the latest challenge, said: "A man with no mandate seeks to cancel parliament for fear it will stop him inflicting on an unwilling public an outcome they did not vote for and do not want.
"That's certainly not democracy and I expect our courts to say it's not the law."
The UK is currently due to leave the EU on 31 October, with the prime minister pledging that Brexit will definitely happen on that day regardless of whether or not a deal has been agreed with the EU.
Most MPs at Westminster are opposed to a no-deal Brexit, and there has been speculation that Mr Johnson could try to get around this by closing parliament in the run-up to 31 October.
This is known as proroguing, and would require the permission of the Queen.
Mr Johnson argued during the Conservative leadership contest that he would not "take anything off the table", saying it would be "absolutely bizarre" for the UK to "weaken its own position" in negotiations with European leaders.
But the group of pro-Remain politicians involved in the legal action at Scotland's highest court argue that shutting down parliament in this manner would be unlawful.
The case is beginning in the Scottish courts because they sit through the summer, unlike their English counterparts.
During a procedural hearing in Edinburgh, lawyers argued that the case could ultimately be decided in the UK Supreme Court - but only after it has moved through the Scottish system.
Lord Doherty refused a motion from the petitioners to skip the first step of this, saying arguments must be heard in the outer house of the Court of Session before they proceed to the next stage, the inner house.
However he did agree to move swiftly, fixing a full hearing for 6 September.
The Commons Speaker John Bercow has said the idea of the parliamentary session ending in order to force through a no-deal Brexit is "simply not going to happen" and that that was "so blindingly obvious it almost doesn't need to be stated".
One of the petitioners, Edinburgh South Labour MP Ian Murray, said: "When Boris Johnson unveiled his vacuous slogan 'taking back control', voters weren't told that this could mean shutting down parliament.
"The prime minister's undemocratic proposal to hold Westminster in contempt simply can't go unchallenged."

"Waited 12 months for that", the prime minister's chief of staff, Gavin Barwell, has just tweeted.
That's both a compliment to his boss, and a revelation perhaps too.
With the complexities of Brexit, the divisions in her party, the calamity of last year's conference speech, the antics of the former foreign secretary, and of course, her own fragilities, Theresa May has struggled to find her voice - and that's got nothing to do with running out of Strepsils.
Well today she found it, and in the words of one of her cabinet colleagues, not a particularly close ally, "she found her mojo".
From the moment she danced on to the stage - who would have thought we'd ever see that - she looked comfortable in her own skin, actually happy to be there.
It sounds strange, but it is so rare to see her overtly enjoying her job.
On so many occasions the public has seen a politician who seems constricted, conflicted, and ill-at-ease. For voters, frankly, if she doesn't look like she is enjoying being prime minister, why should any of us be happy about the fact she's doing it.
Beyond the vital dynamics of the hall, there was a consistent message - this was May the moderate of summer 2016, not May the leader cleaving to one side of her party, the Eurosceptics who have the power to unseat her. A message to her party and the country that in a time of some anxiety, huge uncertainty, and toxic politics, she'll chart a middle course.
There was a big claim that austerity was over. Given that Chancellor Philip Hammond has not got extra cash to throw around and is already looking to raise tax for the NHS, that was a bold claim that may come to haunt the government.
And a direct appeal to Labour voters, and indeed Labour MPs, who may be uncomfortable with the direction of Jeremy Corbyn's travel. Overtly centre-ground stuff, a pitch for an era after Brexit when, perhaps, perhaps, the tensions and bitterness of the last couple of years could fade. That is a big if.
This was a total contrast to last year's disaster. A good outing on the platform doesn't make any of Mrs May's enormous dilemmas disappear. Nor will it magic away the concerns and criticisms of her handling of Brexit.
There are restive forces in her party. She has no majority in Parliament. The Conservatives have huge questions they can't answer about who they are and what they are for.
The fact remains, many of her colleagues simply can't see her taking them into the next election. But Theresa May looks today less like a leader at the total mercy of events, more like a prime minister who knows what she wants and might, just might, have an idea how to get there.

Multiple cabinet ministers expressed significant doubts about the prime minister's preferred Brexit plan from the start, the BBC has learned.
Parts of Theresa May's plan were described as "worrying", "disappointing" and "concerning" by members of her top team back in July.
Mrs May is struggling to broker an agreement on Brexit with ministers.
Two ministers have told the BBC they believe there is little chance the deal would get Parliament's backing.
One of them said it was "self-harming" for the PM to keep pursuing the same strategy.
Mrs May is trying to arrange an agreement in cabinet on the current negotiations in time for a hoped-for summit in Brussels later this month.
Her preferred plan for future relations with the EU after Brexit were agreed at Chequers - the prime minister's country retreat - in July, in a marathon cabinet meeting lasting nearly 12 hours.
Afterwards, Mrs May said the cabinet had reached a "collective" agreement, although former Brexit secretary David Davis and ex-foreign secretary Boris Johnson resigned from the Cabinet in protest at the plans 48 hours later.
And, according to the BBC's political editor Laura Kuenssberg, cabinet sources have now revealed there were widespread doubts about various aspects from many other ministers from the start, including from some former Remain supporters.
For many of those present, she said that the Chequers deal was an undesirable compromise, rather than a set of proposals to which they were signing up with enthusiasm.
One cabinet minister said the group endorsed the proposal "with a very heavy heart".
Trade Secretary Liam Fox expressed strong doubts about elements of the plan for trading arrangements as they could harm the ability of the UK to do trade deals after Brexit.
Home Secretary Sajid Javid, who backed Remain, is understood to have had some similar views, describing the proposal for a common rule book with the EU for parts of the economy as "very worrying" and suggesting that there should be a review of the arrangements after five years.
The leader of the House of Lords, Baroness Evans, is understood to have agreed, telling her colleagues that she found it difficult to accept some aspects of the proposals, and might struggle to explain them in Parliament.
Penny Mordaunt and Esther McVey - Brexiteers who have both been reluctant to give public support for the plan - are said to have expressed significant unhappiness and questioned whether Brexiteer MPs would be able to support such a deal in Parliament.
Meanwhile, Transport Secretary Chris Grayling is said to have warned his colleagues that as many as 40 Eurosceptic MPs might "go on strike".
Sources close to him would not confirm that, but said he had been "extremely cautious from the start" about the Chequers proposal.
And as has previously emerged, the leader of the Commons, Andrea Leadsom, said that she "hated" the proposals and called on the prime minister to treat those who had voted for Brexit with respect.
Chancellor Philip Hammond told his colleagues that the government was living on "borrowed time" because some businesses were hesitating over whether to invest in the UK.
He argued for the Chequers approach to bring clarity as soon as possible. But he is understood to have questioned whether such a deal could actually be achieved, warning that the UK would have to persuade EU member states to defy the European Commission which is running the negotiation.
And the Defence Secretary, Gavin Williamson - also a former Remainer - said there were many concerns with the paper and it must be made clear it was as far as the government would be willing to compromise.
Several ministers on both sides of the argument are understood to have called on the prime minister to be honest with the public about the shift in position towards a closer arrangement with the EU.
Mrs May is trying to arrange an agreement in cabinet on the current negotiations in time for a hoped-for summit in Brussels later this month.
A Number 10 spokesman said: "Everyone has to move a little to get a deal that works for everyone on both sides of the argument."
But Shadow Brexit Secretary Sir Keir Starmer said it appeared Mrs May had proceeded without the "solid backing" of her cabinet, having also declined to get Parliament's support for her negotiating objectives.
Sir Keir also said the option of a fresh referendum was still "on the table", despite Labour's leader Jeremy Corbyn saying at the weekend that Brexit could not be stopped.
In his column for the Daily Telegraph on Monday, Boris Johnson called the prime minister's deal "a recipe for continued strife, both in the Tory Party and the country".
And former cabinet minister John Whittingdale cast doubt on whether Mrs May could stay in office if Parliament rejected any deal she reached with the EU.
"I think if the PM's Brexit plan doesn't get through Parliament, I think it's quite difficult to see how the prime minister can continue because she has staked her credibility," he told BBC Radio 4's Westminster Hour.

Often the hype about a political event is in inverse proportion to the drama of what actually comes to pass. Maybe not this time.
Cabinet ministers will today meet at Chequers with the aim of approving the prime minister's blueprint for the UK's future relationship with the EU after Brexit.
But Brexiteer ministers have warned that the 120-page plan as written is flawed. They were discussing late on Thursday how to respond during the cabinet meeting.
And to say that they are a bit miffed with the plan, which they only received in its entirety on Thursday afternoon, is an understatement. There is plenty in there that they don't like, and it's easy to see why.
The BBC understands that the plan includes:
The paper also suggests that, while trade deals with other countries like the US would be possible, they might be harder to do because under rules agreed with the EU, it would be harder to meet other countries' "asks".
One cabinet minister also expressed unhappiness with the proposed customs model - the facilitated customs arrangement - saying that it was like "customs partnership minus" - simply a revision of the customs partnership model that was rejected by the inner Brexit cabinet committee weeks ago.
One senior Tory suggested that "the party wouldn't wear it". A senior Brexiteer minister said that a lot of the document was "problematic", and that there was a "lot of scope for argument".
Essentially, for those who want a dramatic break with the EU, it falls far short, even though Number 10 insists it is merely an evolution of what the prime minister has already promised.
Frankly, from what we have heard, language is doing a lot of the heavy lifting, with much of it "opaque".
It does sketch out a relationship with the EU that is much tighter than Brexiteers had argued for. Would it really be Brexit? Number 10 would say yes, Jacob Rees Mogg would say no.
For the rest of us? That depends what you think the country voted for.
Tension around the meeting is high, with ministers being instructed in an email that they will have to hand in their phones and Apple watches on arrival at Chequers.
Brexiteer ministers shared concerns at a meeting in the foreign secretary's office on Thursday night over the plan, with a source saying "it's not going to fly".
They said that they will "simply reject it if she tries formally to impose it". But another Brexiteer source said they would have to "talk it out" before coming to any conclusions about the plan.
But a cabinet minister who has been pushing for a tight relationship with the EU told the BBC that while the plan was "fiendishly complicated... no one had a better idea".
A former cabinet minister who advocates closer ties to the EU told the BBC that they had urged the prime minister to consider sacking Brexiteers who refuse to sign up.
They suggested that "blood on the carpet" might not be a bad thing. They said they believed the prime minister "has had enough steel put in her spine" to be able to command ministers to back her plan or carry out a reshuffle.
There is however concern in the City, too, over the suggestion of giving up the prospect of a close deal on services to guarantee an end to free movement. One insider suggested that Chancellor Philip Hammond may try to "wedge" services back into the draft agreement on Friday.
Sources on all sides of the argument suggest that it is too early to tell how the talks tomorrow will end. There are demands for "significant redrafting". The discussions start at around 10:00 BST and are expected to wrap up at about 22:00 BST.
Insiders also suggest that with the EU likely to reject much of the plan, the real debate will focus on what to do if and when Brussels says no, with Brexiteers pushing a "Canada plus" model.
Another cabinet minister told the BBC that even though the EU was unlikely to accept it straight off, the point of this week's talks was not to find a final agreement, but simply to "start a conversation" with Brussels so that vital talks on the future relationship can get going.
Until now, the negotiations have focused on the withdrawal agreement - the divorce deal - with no formal engagements over the long-term arrangements. An outline of the political agreement on that deal is supposed to be in place by October.
To have any hope of a genuine and substantial deal by the autumn, the prime minister needs Brussels to take her, and her approach, seriously. If she fails to get agreement, her ability to project the authority that's needed for that to happen will be seriously put into question.
But if she pushes ahead with the plan she will have to face down a powerful and vocal wing in her party.
Some of her colleagues might heave a huge sigh of relief, and think, "about time too". But her party, and the rest of us, have no way of knowing tonight if that decision - which would risk her leadership - is one she is really willing to take.

Theresa May has called for discussions about future NHS funding to remain private after Boris Johnson publicly called for more money after Brexit.
Before Tuesday's cabinet meeting, it was widely reported that the foreign secretary would pitch for a £100m a week "Brexit dividend" for the NHS.
The BBC understands he did not end up mentioning "specific figures".
No 10 said Mrs May chaired a discussion on post-Brexit funding options but made clear conversations should be private.
The BBC's political editor Laura Kuenssberg said the PM's remarks on the need for confidentiality were "pointed".
However, she said Mr Johnson was backed by some colleagues while the principle that the NHS would get some of the money which will become available after the UK leaves in March 2019 was agreed.
In the run-up to Tuesday's cabinet meeting - in which Health Secretary Jeremy Hunt gave an update on the "significant" winter pressures" facing the NHS - it was reported that Mr Johnson wanted to kick start a wider debate about NHS funding.
In a highly unusual move, sources told the BBC Mr Johnson would not only call for a £5bn annual injection of funding after Brexit but warn his party against "abandoning the territory" to Labour, which vowed at last year's election to spend £37bn more over the next five years.
If you can't see the NHS Tracker, click or tap here.
A source close to Mr Johnson said he was frustrated at what he perceived as Downing Street's lack of action on the issue given the levels of public anxiety about how the NHS is faring.
During the referendum campaign, Vote Leave - of which Mr Johnson was a leading supporter - claimed £350m went to the EU each week and money could instead go to the NHS, a claim he has repeatedly defended since.
However, when it came to it, the BBC's assistant political editor Norman Smith said neither Mr Johnson nor any other minister raised a specific figure during what No 10 said was a "wide ranging" hour-long discussion.
Firmly, in one sense.
A No 10 spokesman said the prime minister and "a large number of Cabinet ministers" had made clear that their discussions should take place in private.
On the broader political point, Downing Street said the PM reminded ministers that the government has repeatedly said contributions to the EU budget which end after Brexit would be able to be spent on domestic priorities including the NHS.
"There will also be other calls upon that money but we will discuss those priorities at that time," a spokesman said.
In a further rebuff to Mr Johnson, Chancellor Philip Hammond said he had given the NHS an extra £6bn in November's Budget, including £2.8bn to be spent over the next two years,
Mr Hammond, who was in Brussels for a meeting of EU finance ministers, told reporters Mr Johnson was "the foreign secretary" not health secretary and the right time to revisit the long-term issue of NHS spending was at the next departmental spending review expected early next year.
No, far from it. The BBC understands that Chris Grayling and Michael Gove were among other cabinet ministers to rally round Mr Johnson at Tuesday's meeting.
Growing numbers of Tory MPs are openly expressing their frustration with what they say is No 10's unwillingness to confront the long-term financial challenges facing the health service.
Conservative MP Mark Pritchard told the BBC News Channel the foreign secretary was right to speak out.
"I support Boris, he's right. But I think whether it's Boris or Theresa May or Jeremy Hunt, in the longer term there needs to be political leadership about how we fund the NHS going forward in the twenty-first century."
As for Jeremy Hunt, he said no health secretary would "not support potential extra resources" for the NHS.
Asked how he felt about Mr Johnson being the one to make the case, he said there was "a Brexit debate and an NHS debate and just occasionally these two debates come together".
Labour's shadow health secretary Jonathan Ashworth said he welcomed calls for more funding but accused Mr Johnson of seeking to "weaponise" the NHS for his own "tedious political games".
"If the government was really serious about putting money into the NHS, they would have done it in the Budget last autumn," he told the BBC's Victoria Derbyshire show. "We did not hear a peep from him then."
The Institute for Fiscal Studies - a think tank - has said the UK will almost certainly have to increase the share of income devoted to health funding to deal with demographic challenges.
Its director Paul Johnson said "that will mean higher taxes" and "governments will need to explain that honestly".
Lib Dem leader Vince Cable suggested Mr Johnson and his colleagues begin this process now.

The future relationship between the UK and the EU will not be negotiated within two years, says the former head of the Foreign Office.
Separation talks could be completed within the two year deadline set out in Article 50, but a future relationship would take longer to negotiate, Sir Simon Fraser told BBC Newsnight.
Sir Simon said "transitional arrangements" would be necessary.
Prime Minister Theresa May will invoke Article 50 on Wednesday.
"It's certain that we won't have resolved everything in the period before the expiry of the Article 50 process," Sir Simon Fraser told BBC Newsnight.
"The EU side want to start with negotiating the terms of the separation... And the British side, on top of that, wants to move rapidly to discuss the future relationship - both political and economic - between Britain and the EU. And that is a very complex second set of negotiations."
Because of the difficulty of defining the future relationship, Sir Simon, who held senior posts in Brussels and Whitehall before becoming the head of the diplomatic service, believes talks will soon shift to the nature of 'transitional arrangements'. This means vital questions about how the UK does business with the EU could be left unresolved far beyond 2019.
Many Brexit supporters had hoped informal negotiations with the EU could start before the Article 50 clock begins ticking this week. Negotiations are limited to two years.
But Sir Simon said the European Commission has thwarted such plans: "There has been a very disciplined position across the EU, and I don't think that there has been a lot of informal behind the scenes discussion of the agenda or of the key issues yet."
Sir Simon is also sceptical that the UK will be able to play off different countries among the EU's 27 countries.
"The UK has got to negotiate with the EU as a whole through the EU's appointed negotiator, which will be essentially led by the Commission."
He added: "I think it would be a mistake to try divide and rule because I don't think that that will work."
While Article 50 allows up to two years to reach an agreement, the EU's chief negotiator, Michel Barnier, has said he wants the outline of a deal to be ready by autumn 2018, in the hope that it can then go before the European Parliament for ratification and member states for agreement well before the deadline is up.
But many diplomats, Sir Simon Fraser among them, believe that there will be no serious political discussions before this autumn, following the German elections.
While Brexit dominates national debate in the UK, it is a secondary issue for many European governments.
This could lead to delays in negotiations with many governments not taking positions until they have to. Combined with the complexity of the Brexit discussions, many diplomats believe that the UK could find itself close to a "cliff edge" without final agreement.
Sir Simon said while it was in the interest of both sides to avoid such a scenario, there was a "risk of political ill will and turbulence - both political and economic" if a deal is not reached within the Article 50 timeframe.
It is for this reason that Mr Barnier may want to make transitional arrangements dependent on a resolution of one of the first items on the EU's divorce agenda: getting the UK to agree to paying a bill of tens of billions into the Commission's coffers.
Mark Urban is diplomatic and defence editor for BBC Newsnight

Home Secretary Amber Rudd has appeared to cast doubt on the government's policy of not being in a customs union with the EU after Brexit.
She told journalists she would not be "drawn" on the issue and said there were discussions to be had about it in cabinet to agree a "final position".
Later she tweeted that she "should have been clearer" but had not wanted to get into "ongoing cabinet discussions".
The PM Theresa May has ruled out being in an EU customs union after Brexit.
The comments came on the day Ms Rudd faced fresh calls to resign over her handling of the Windrush scandal, which has seen relatives of people from Caribbean countries who settled in the UK decades ago being declared illegal immigrants, if they could not prove they had lived continuously in the UK.
She was forced to admit in the House of Commons that immigration removal targets had existed, a day after telling a committee of MPs that there weren't any.
But the issue of whether or not the UK would be in a customs union after Brexit came up as she addressed a lunch for parliamentary journalists
She replied: "I'm not going to be drawn on that. We still have a few discussions to be had in a really positive, consensual and easy way among some of my cabinet colleagues in order to arrive at a final position."
Labour's Sir Keir Starmer said: "Amber Rudd appears to have let slip that discussions around the cabinet table about negotiating a customs union with the EU have not in fact concluded.
"If that is so, then the prime minister should rethink her approach and listen to the growing chorus of voices in Parliament and in the businesses community that believe she has got it wrong on a customs union."
And Tory backbencher Peter Bone tweeted:
Ms Rudd later tweeted a clarification:
The prime minister is under pressure from both sides of the EU debate on the issue of the customs union, which allows for goods to be transported tariff-free between EU member states.
The Financial Times reports that Mrs May is expected to try to secure agreement on an alternative to the customs union, in a Brexit cabinet committee meeting next week.
Ministers were defeated on the issue in the House of Lords last week and the government faces key votes in the Commons next month.
On Thursday, the prime minister's spokesman said: "The government is clear we are leaving the customs union and not joining a customs union."
Brexiteers have criticised a suggested "customs partnership" to replace the current arrangements, while pro-EU campaigners say a customs union is the only way to prevent a hard border in Northern Ireland.
MPs debated a non-binding motion on Thursday calling on the government to include in its negotiating objectives with the EU "the establishment of an effective customs union between the two territories".
With few pro-Brexit MPs attending the debate, the motion was approved without a vote, prompting Labour's Chris Leslie to suggest it "was now the default consensus view of this House" and said the government should respond.
Crunch votes are expected next month when Remain-supporting MPs will push for a change of course.
A customs union is when countries agree to apply the same taxes on imports to goods from outside the union.
This means when goods have cleared customs in one country, they can be shipped to others in the union without further tariffs being imposed.
If the UK remains part of the customs union, it would be unable to strike trade deals with countries around the world, but supporters say it would help keep an open border between Ireland and Northern Ireland.
During the debate, Labour's Yvette Cooper said the UK exported more than £230bn of goods and services to the EU every year and warned that to "rip up" existing trade arrangements would be "deeply damaging".
She argued that existing trade deals should be "cherished" as it was becoming harder to negotiate new ones "as communities across different individual countries become more worried about both the losers and the winners of big changes to trade arrangements".
Pro-European Conservative Ken Clarke told MPs: "You will damage the economy of this country... if you suddenly decide to erect new barriers at the border between the UK and our major trading partners."
And former Conservative cabinet minister Nicky Morgan warned: "If we undermine and ignore the evidence for peace in Northern Ireland, and we undermine the business and financial security of the people in this country, we will not be forgiven for a generation."
Labour MP Kate Hoey, one of the few Brexiteers at the debate, said she felt "alone" in the chamber: "There are a lot of people here today who are using the issue of the customs union to start the process again of wanting to stay in the European Union."
She argued that if the UK stayed in the customs union, it would be a "transition" to remaining, and would not allow Britain to "take back control" of its trade.
Labour leader Jeremy Corbyn has backed a customs union, but only if the UK had a say in future EU trade deals.
Mrs May has ruled out joining a customs union but has come up with two options to avoid a hard border in Ireland.
One of them is a "customs partnership" that would involve the UK collecting the EU's tariffs on goods coming from other countries on the EU's behalf.
If those goods didn't leave the UK and UK tariffs were lower, companies could then claim back the difference.
This option has been heavily criticised by some Brexiteers, with influential backbench Tory MP Jacob Rees-Mogg branding it "completely cretinous".
The other option being proposed by the government would be to minimise checks rather than getting rid of them altogether, by using new technologies and putting in place a trusted trader scheme.

Boris Johnson has warned EU leaders not to give the UK "punishment beatings" for Brexit "in the manner of some World War Two movie".
The foreign secretary said penalising "escape" was "not in the interests of our friends and our partners".
PM Theresa May set out her Brexit strategy, including leaving the EU single market, in a speech on Tuesday.
European Commission President Jean-Claude Juncker promised to work for "good results" from Brexit talks.
Meanwhile, the Supreme Court has announced it will give its verdict next Tuesday on the government's legal battle over whether MPs must be consulted before Brexit is triggered.
And HSBC announced it was preparing to move 1,000 staff from London to Paris when the UK leaves the EU.
At Prime Minister's Questions, Mrs May clashed with Labour leader Jeremy Corbyn, telling him she had a "plan" and he did not "have a clue".
Mr Corbyn accused her of "threatening to turn Britain into an offshore tax haven".
With just over two months to go before the UK government is due to get Brexit talks under way, Mr Johnson was asked on a trip to India about comments by an aide to French President Francois Hollande, who said the UK should not expect a better trading relationship with the EU after leaving it.
He replied: "If Monsieur Hollande wants to administer punishment beatings to anybody who chooses to escape, rather in the manner of some World War Two movie, then I don't think that is the way forward.
"I think, actually, it's not in the interests of our friends and our partners."
Downing Street later said Mr Johnson "was not in any way suggesting anyone was a Nazi".
The spokeswoman said the remarks were "all being hyped up" and that the foreign secretary had used a "theatrical comparison", adding: "There is not a government policy of not talking about the War."
But a Labour spokesman said: "The foreign secretary has a habit of making wild and inappropriate comments. Talking about World War Two in that context is another one of those and not something that's going to improve the climate for negotiations."
Former cabinet minister and Brexit campaigner Michael Gove hit back, tweeting that people offended by Mr Johnson's "witty metaphor" were "humourless, deliberately obtuse, snowflakes".
EU leaders have begun to deliver their verdicts on Mrs May's speech, in which she also warned against trying to "punish" the UK for Brexit and hinted she could walk away from talks if not happy, stating that "no deal for Britain is better than a bad deal for Britain".
German Chancellor Angela Merkel said: "The be-all and end-all is that Europe does not let itself be divided, and we will ensure that with very intensive contacts.'' EU governments would consult their business sectors, she added, and she was "not worried that we will not stick together".
Mr Juncker said he would work to ensure Brexit talks are carried out "according to the rules and they yield good results".
He added: "I welcome the clarifications given by Mrs May, but I said to her last night that a speech will not launch the negotiations."
Analysis - By James Landale, BBC diplomatic correspondent
Not surprisingly, uproar has ensued.
Former Labour leader Ed Miliband said Boris Johnson had shown once again that he could be "supremely clever and yet immensely stupid".
To some Britons, Mr Johnson's remarks will be seen as colourful but unexceptional language that echoes the popular World War Two film The Great Escape.
To many of Mr Johnson's generation, these films were part of their childhood and are subject to frequent cultural reference. Former Prime Minister David Cameron has seen The Guns of Navarone more than 17 times and once quoted a line from the film in a party conference speech.
Read James's blog in full
Guy Verhofstadt, the European Parliament's lead Brexit negotiator, said: "You can say, 'I want to leave the European Union, I want to leave the judicial courts, I want to leave the customs union.'
"But you cannot at the same time then say, 'Oh, and that little piece that interests me, and that is something that I like.' No way."
However, European Council President Donald Tusk was more conciliatory, tweeting: "We took note of Prime Minister May's warm, balanced words on European integration. Much closer to narrative of Churchill than President-elect Trump."
Downing Street said European leaders spoken to by Mrs May in a series of phone calls had welcomed the "clarity" of her plans.
In its headline, the Times sums up the prime minister's message to the EU as "Give us a fair deal or you'll be crushed".
Meanwhile, the Brexit-supporting Daily Mail draws parallels with Margaret Thatcher, saying Mrs May exhibited the "steel of the new Iron Lady".
The Guardian, which opposed Brexit in the referendum, found the speech a "doubly depressing event" - a reality check for those who want to keep the UK in the single market while being riddled with its own streak of "global fantasy".
The Financial Times praises the prime minister's "bold vision" but warns that the road ahead will be perilous.
The Sun's front page is mocked up as a Biblical tablet of stone bearing the single-word headline "Brexodus".
Read The Papers in full
In her speech, the prime minister suggested the UK could cut its corporate tax rates to compete with the EU if denied access to the single market.
And she promised that Parliament would get to vote on the final Brexit deal.
Asked what would happen if MPs and peers rejected it, Brexit Secretary David Davis told Today: "They won't vote it down. This negotiation will succeed. It will succeed."
The government says it will invoke Article 50 of the Lisbon Treaty, getting formal Brexit talks with the EU under way, by the end of March, with discussions set to last up to two years after that.
A "catalogue of demands with some threats thrown in" is German news magazine Der Spiegel's description of Theresa May's Brexit speech. It says that her desire to leave the single market while retaining access to trade with Europe shows that her government is "not just nasty but also blind to reality".
Germany's Die Welt also mocks her with the headline "Little Britain" and accuses her of leading the country into "isolation".
In Italy, La Repubblica's front page reads "Brexit: London raises its wall 'away from the EU and the single market'".
France's Liberation remarks that Mrs May's comment that no deal is better than a bad one suggests that she is threatening to turn Britain into a tax haven. "If this is not blackmail, it looks a lot like it," it says.
At Prime Minister's Questions, Mr Corbyn urged Mrs May to "stop her threat of a bargain basement Brexit, a low-paid tax haven on the shores of Europe".
He added: "It won't necessarily damage the EU but it would certainly damage this country."
Mrs May told MPs:  "What I set out yesterday was a plan for a global Britain, bringing prosperity to this country and jobs to people and spreading economic growth across this country."
UKIP leader Paul Nuttall said: "It's clear that Britain is going global, as a result of that momentous [EU referendum] vote on 23 June."

The EU Commission President, Jean-Claude Juncker, has urged Belgium to grant citizenship to British EU staff worried about their post-Brexit status.
About 1,100 UK citizens work for the EU in Brussels and Luxembourg.
Mr Juncker called Belgium a kind host and asked its prime minister, Charles Michel, to "show the same generosity when it comes to granting Belgian citizenship" to British EU staff.
When the UK leaves the EU next March Britons will lose their EU citizenship.
The UK and EU have already pledged to protect citizens' rights after Brexit, but that does not mean granting nationality.
Article 49 of the EU staff rules states that "an official may be required to resign" if he or she loses their EU citizenship and is no longer a national of an EU member state.
Many British EU staff are longstanding residents with families.
An internal EU Commission document quoted by Politico news last month said Article 49 would not mean British staff losing their EU jobs, apart from cases involving "conflicts of interest or international obligations".
Responding to Mr Juncker's plea during a European Parliament debate, Mr Michel said Belgium's citizenship law in the context of Brexit was "contradictory", but he did not specify the difficulties.
"The government is examining the judicial possibilities on this question, which affects a number of people who have been living in our country for a long time," he said.
European Commission spokesman Margaritis Schinas said later that Mr Juncker's remarks were meant as a reminder for the Belgian leader. "We live up to the promise that our colleagues of British nationality should be given maximum guarantees to stay, not only with their employment but also if they want to stay as Belgian citizens. But this is entirely in the hands of the Belgian government, not ours," he said.
EU citizenship is described in Article 20 of the Treaty on the Functioning of the European Union and includes the rights to:
Michael Ashbrook of Solidarity, Independence, Democracy (SID), a trade union representing EU staff, told the BBC that "all the British staff are trying for EU citizenship". "They are very worried", he said, referring to the impact of Brexit on their jobs.
"There has been talk of dismissing British 'contract agents' on Brexit day, rather than letting them complete their fixed-term contracts," he said.
Resolving the status of British staff, to keep them in their jobs, would take the Commission "just a few minutes", he said.
Brexit sets a legal precedent for the EU and raises a host of new legal challenges, because no state has left the 28-nation bloc before.
In the debate the Belgian leader clashed with UKIP's Nigel Farage, an anti-EU MEP.
"Belgium is not a nation; it's an artificial creation," Mr Farage said. The Dutch- and French-speaking parts of Belgium "dislike each other intensely", he alleged.
Mr Michel replied ironically: "I'm happy to hear this sound advice from Nigel Farage on the future of Belgium. He has been busy with the future of Britain, with Brexit - and we can see where Britain has got to with that."
To qualify for Belgian citizenship, an applicant must have lived in Belgium for at least five years legally and passed a language test.
Luxembourg requires at least five years' residence and competence in Luxembourgish, a language with only about 390,000 native speakers.

Businesses will not have to carry out new checks on EU staff in the event of a no-deal Brexit, the government says.
"Employers will not be expected to differentiate between resident EU citizens and those arriving after exit," the Home Office said.
On Tuesday, minister Caroline Nokes said employers would have to carry out "rigorous checks" on EU staff who arrived after March 2019.
Labour accused her of misleading Parliament.
Shadow immigration minister Afzal Khan suggested Ms Nokes lacked "even the most basic level of understanding and knowledge" of her own immigration policy and demanded she "come to Parliament to set the record straight".
The government insists EU free movement will end in March 2019, the scheduled date for the UK's departure from the EU.
But in practice, EU nationals will still be able to come and work in the UK, until the end of the planned 21-month "transition period". The only difference is that they will have to register with the authorities.
Ms Nokes was questioned at length on Tuesday about what would happen if there was no "transition period" - because the UK leaves the EU without having agreed a withdrawal deal - and whether employers would be expected to check if potential staff had the right to work in the UK.
Committee chair Yvette Cooper asked how an employer could be expected to differentiate between someone who had arrived in the UK after Brexit - and an EU citizen who had been a long term resident and had the right to work, but had not yet applied for "settled status".
Ms Nokes admitted it would be "almost impossible for an employer to differentiate between a new arrival and somebody who has been here for 10 years and has simply not yet been through the scheme".
But she said: "If somebody has been through the settled status scheme, they will be able to evidence that. If somebody has not been here prior to the end of March next year, then employers will have to make sure that they go through adequately rigorous checks to evidence somebody's right to work."
Her remarks were met with "deep concern" from the Federation of Small Businesses, whose chairman Mike Cherry said:  "The reality is that many of these businesses wouldn't have the first idea of where, or how, to check whether or not their EU staff have the right to work here."
The 3million, which campaigns for the rights of EU citizens in the UK, reported that the Home Office had emailed to confirm current checks "will not change next March in the event we leave the EU without a deal".
And that "EU citizens will continue to be able to evidence their right to work by showing a passport or national identity card." Employers would not be expected to differentiate between "resident EU citizens and those arriving after exit".
On Friday, the Home Office confirmed that statement and added: "We will protect EU citizens' rights when we leave the EU, in both a deal or no deal scenario.
"We are considering a number of options for the unlikely event that we reach March 2019 without a deal, and will set out more information shortly."
Under current rules, employers must carry out "right to work" checks on new staff.
For British citizens, this means providing a passport or birth certificate and a National Insurance number while EU citizens must provide their passport or ID card and people from outside the EU must provide their biometric residence permit.

We all know what it's like - having to play nice with the person you don't have very much in common with, because it's the right thing to do.
Knowing that lots of people you DO like would be upset if you don't put on a show.
Well, how about this: having to "play nice" publicly with a person you don't have very much in common with, when they have said that the way you are trying to do your job doesn't really work.
Add in the embarrassment if they happen to be the leader of the free world.
From the moment of his election, Donald Trump was an awkward friend for Theresa May.
He runs towards a fight. She does everything in public to avoid one.
Well, just before they were due to appear alongside each other on UK soil he publicly, and at length, gave a "both barrels" verdict on her most important policy.
Her approach to Brexit has been to slowly, gently, incrementally, carry the Ming vase across one side of the room to another on a slippery floor.
To talk about being pragmatic, to smooth over the contradictions, to do whatever it takes to get to the other side, without smashing that vase (her party and the country) to bits.
In walks President Trump, to call out one of the claims that No 10 has been making of late - in essence, smashing the vase to bits.
In an interview with The Sun, he shoots down the chances of a trade deal with the US if she sticks to her carefully crafted compromise Brexit plan.
That matters because the government has been clinging to the idea of trade deals with countries outside the EU as one of the benefits of Brexit, and claiming that the choice in the Chequers deal to stay close to the EU doesn't exclude those opportunities.
This isn't about what side anyone was on in the referendum. In fact, Remainers and Leavers unite in saying the Chequers deal can't live up to all it claims.
For former Remainers, it's nuts to think that trade deals with non-EU countries can ever make up for what might be lost.
For some Leavers, it's nuts to claim we can make the most of the world outside if we are still sticking to EU rules.
And President Trump drives a bulldozer through the government's central claims about its compromise - that the UK would be able to get decent trade deals with the wider world, while sticking to the EU rules.
A lot of this visit has been carefully choreographed, as the prime minister and the president dance around each other.
But if the president really wanted to help her build support for her controversial compromise, this isn't the way to do it.

The UK would be welcome to stay in the EU if it changed its mind about Brexit, Donald Tusk has suggested.
The European Council President told MEPs that the UK would leave the bloc unless it had a "change of heart".
"We haven't had a change of heart. Our hearts are still open for you."
The comments were welcomed by MPs who want a referendum on the final Brexit deal but Environment Secretary Michael Gove said the British public had voted in record numbers to leave the EU.
"We have a great future outside the European Union and we should be embracing that," he said.
The government has said there will be no second vote ahead of the UK's exit in March 2019.
Labour leader Jeremy Corbyn has also dismissed the idea while insisting that MPs have a "meaningful vote" in Parliament on the terms of the withdrawal agreement.
Former UKIP leader Nigel Farage has said the prospect of a second vote cannot be ruled out, although he was confident it would return a larger margin for Leave than in 2016 - when 17.4 million people voted for Brexit.
The EU, he told BBC World Service, was intent on "putting something on the table so unattractive to Britain that Parliament will vote for us to have a second referendum".
As it stands, the UK is due to leave the EU in March 2019.
The two sides reached a deal on so-called "divorce issues", including money and citizens' rights, in December and talks are now moving onto transitional arrangements and future co-operation.
Revised draft EU guidelines obtained by several UK newspapers suggest the EU is toughening its stance on what changes the UK can make on immigration, trade and fishing during a roughly two year transition period.
Speaking in the European Parliament in Strasbourg, Mr Tusk said he believed the other 27 EU members would maintain their unity when the talks resumed in March.
"The hardest work is still ahead of us, and time is limited," he said.
"If the UK government sticks to its decision to leave, Brexit will become a reality - with all its negative consequences - in March next year. Unless there is a change of heart among our British friends.
"Wasn't it David Davis himself who said 'if a democracy cannot change its mind, it ceases to be a democracy'.
"We, here on the continent, haven't had a change of heart. Our hearts are still open to you."
Former Lib Dem leader Nick Clegg, who has said Parliament should have the power to reject any deal reached and force ministers back to the negotiating table, welcomed Mr Tusk's remarks.
Labour MP Daniel Zeichner, a supporter of the Best for Britain group, which was launched last year by pro-EU campaigner Gina Miller, said the option to remain in the EU must be kept open.
"We are stronger together, and it becomes increasingly clear that the current path is extremely damaging," he said.
But Leave Means Leave, which grew out of the Vote Leave campaign during the 2016 referendum, said Brussels had a history of not listening to the views of voters.
"Donald Tusk and Jean-Claude Juncker need to accept that Britain is a democracy - something the EU knows very little about," said its co-chair Richard Tice.
"The British people voted to leave the EU and this decision will not be reversed, despite their best efforts."
Mr Tusk's sentiments were also dismissed by prominent Brexiteers in the European Parliament.

David Davis has hit out at the EU over its decision to exclude the UK from the Galileo satellite navigation system.
The Brexit secretary accused the European Commission of "shooting itself in the foot just to prove that the gun works".
He said throwing the UK out of Galileo would delay it by three years and cost the EU £1bn more.
The UK has played a major role in developing satellites for Galileo, an alternative to the US GPS system.
But Brussels has cited legal issues about sharing sensitive information with a non-member state for its decision to shut British firms out of the project. Brussels has also said it will restrict access to encrypted signals from Galileo.
The move has sparked a furious reaction from the UK government, which is demanding £1bn back from the EU and has threatened to build a rival satellite system, at an estimated cost of £5bn.
In a speech on post-Brexit security co-operation, Mr Davis said: "We should be able, as trusted allies and friends of Europe to get an agreement that allows sensitive information to be shared."
He said British companies were being discriminated against and blocked from contracts - despite the fact that excluding the UK would delay Galileo by three years or more.
"This is not an issue isolated to Galileo," he added.
"The same is at risk of happening with the new European Defence Fund."
The UK had originally opposed the creation of the European Defence Fund, which co-ordinates joint operations by member states.
The government wants to continue contributing troops, equipment and money to overseas EU military operations after Brexit.
But Mr Davis said the EU's attitude to "third countries" - which the UK will become after Brexit - was standing in the way of that ambition.
"All of these unhelpful precedents and assumptions on how third countries should operate with the EU is hindering projects that would help the entire continent," he said in his speech.
The UK had also opposed the creation of Galileo, when it was first proposed 18 years ago, but Britain's space industry had been a major player in the project, which is meant to be fully operational by 2026.
It comes as the European Commission announced plans to pump an extra €5bn (£4.4bn) into space projects, including Galileo and the Copernicus Earth Observation Programme, which will be delivered in partnership with the European Space Agency.
Britain will remain a member of the European Space Agency, which is not an EU body, after Brexit, and is willing to pay a fee of around £1bn to the European Commission to remain part of its space plans.
But the Commission's spending proposals on are based on the assumption that it will get no more cash from the UK after Brexit.

A Welsh Conservative MP has quit as a minister in anger at concessions being given to Brexiteers by Theresa May.
Guto Bebb resigned as minister for defence procurement in order to vote against the government on amendments it accepted to its Brexit Customs Bill.
MPs voted 305 to 302 on Monday to back a change Remainers said would undermine Mrs May's negotiating position.
Welsh Secretary Alun Cairns said he was "very sorry" the Aberconwy MP felt he had to resign over the issue.
Mr Bebb had staunchly defended the prime minister amid the turmoil which has followed the unveiling of her blueprint for post-Brexit relations with the EU.
He branded Boris Johnson's resignation as foreign secretary "a selfish act" and attacked former Brexit Minister David Jones for criticising Mrs May's plan.
Mr Cairns told BBC Radio Wales he was "going to miss" Mr Bebb, who had served under him as a junior Wales Office minister.
Speaking on Good Morning Wales, he said: "Guto was an excellent minister and a close colleague and a good friend.
"I'm very sorry that he felt in order to vote last night that he needed to leave the government."
Glyn Davies, Conservative MP for Montgomeryshire, said: "I am very upset that Guto has felt the need to resign from the government. He is a good friend and was an outstanding minister.
"Guto is a man of deep principle. He is such a talented politician that I cannot believe he will not find another important role in the future."
Leave campaigner and Monmouth Conservative MP David Davies said he was "sad to see him go", adding: "He's a friend and he was doing a really good job in the MoD [Ministry of Defence].
"Guto is strong-minded though and in some ways I'm not surprised."
Mr Bebb was appointed minister for defence procurement in January 2018 after serving as parliamentary under secretary of state at the Wales Office and a government whip from March 2016.
He was elected MP for Aberconwy in May 2010 and voted Remain in the 2016 EU referendum.
The Customs Bill amendment was tabled by Brexiteer Tories and the government's backing of it sparked a backlash from pro-EU Tory MPs, who said the PM had "capitulated".
But Downing Street, which agreed to accept the four amendments, said they were "consistent" with the White Paper where it sets out how it wants to trade with the EU in years to come.
MPs backed the amendment that prevents the UK from collecting taxes on behalf of the EU unless the rest of the EU does the same for the UK.
Applying EU tariffs to products destined for the EU is part of Mrs May's plan to avoid friction at UK borders after Brexit.
Another amendment, to ensure the UK is out of the EU's VAT regime, was backed by 303 to 300.
Clwyd West MP David Jones - a former Brexit minister and Welsh secretary who led the Vote Leave campaign in Wales - said the government was right to listen to its Brexiteer critics but believed "a lot more listening" needed to be done.
Guto Bebb voted Remain in the Brexit referendum and it was no secret he had become increasingly frustrated by the actions of some of the Brexiteers in his party.
He accused former Brexit Minister David Jones of sour grapes after he criticised the prime minister's plan for future trade with the EU.
He also attacked senior cabinet ministers for "inflammatory" and "unworthy" comments after then-Health Secretary Jeremy Hunt said threats from business over Brexit were "inappropriate".
But after a string of resignations by Brexiteers, Guto Bebb's decision to leave a job he obviously enjoyed has surprised many.
What may seem strange is that he resigned so he could vote for what was the prime minister's own position a few hours earlier.

The DUP did not like what was proposed on "regulatory alignment", but Brexit Secretary David Davis suggests that the concept will still be key to making progress.
"Regulatory alignment" effectively means continuing to follow at least some of the rules of the EU's single market.
The taoiseach (Irish prime minister) said that the EU and UK had agreed that, short of a comprehensive trade agreement, there would be ongoing alignment between the two parts of Ireland sufficient to avoid a hard border.
In his answer he explained what he understood by the term.
He referred Mrs Cooper to the prime minister's Florence speech, in which Theresa May spoke about how the EU and UK "share a commitment to high regulatory standards".
Mr Davis said the Prime Minister had made the case that the two sides would, in some areas, want to reach the same regulatory outcomes, but by different methods.
This is a concept which the the UK government had previously proposed.
In its paper on Northern Ireland, published earlier this year, it raised the idea of regulatory equivalence on agri-food measures.
It stated that the UK and the EU could agree to achieve "the same outcome and high standards, with scope for flexibility in relation to the method for achieving this".
Mr Davis went on to to say that this sort of alignment would apply to the whole of the United Kingdom, rather than just Northern Ireland.
The Scottish Conservatives leader, Ruth Davidson, expanded on this point in a statement.
"If regulatory alignment in a number of specific areas is the requirement for a frictionless border, then the prime minister should conclude this must be on a UK-wide basis," she said.
So perhaps the government thinks they can persuade the DUP that regulatory alignment will be something for the UK as a whole, not just Northern Ireland.
However, there could be a difficulty with this all-UK approach, as the Institute for Government pointed out in a recent report, subtitled "Can the UK have its Brexit cake and eat it?'"
It points out that while the UK is trying to reassure the EU that it intends to meet the same regulatory outcomes it is also talking about having "flexibility" on the legal rules and standards underpinning them.
The institute suggests that the EU may interpret flexibility as a risk to its environmental, social and health and safety standards.
For example, in August the EU's chief negotiator Michel Barnier said: "The UK wants to take back control, it wants to adopt its own standards and regulations.
"But it also wants to have these standards recognised automatically in the EU... This is simply impossible."
The EU has been consistent in its belief that Northern Ireland will need a special deal to cater to its unique circumstances.
But it has been equally clear that such a deal cannot apply across the UK as a whole.

Tory MP Jacob Rees-Mogg has called for a fundamental change in ministers' tone on Brexit, accusing UK negotiators of being "cowed by the EU".
The Eurosceptic backbencher said in a speech that "close alignment" with the EU after Brexit would be unacceptable.
Chancellor Philip Hammond, meanwhile, has said he hopes the UK and EU economies will only move "very modestly" apart after Brexit.
He said they were already "completely interconnected and aligned".
BBC political editor Laura Kuenssberg said the war of words went right to the heart of Mrs May's struggle to keep her party together over its biggest project - how the UK will leave the EU.
While the majority of ministers thought she was the only person able to do it, the mood in the party had turned sour in recent weeks with one senior Conservative MP saying they were "in the mood for regime change".
The UK is due to leave the European Union in March 2019, and negotiations are taking place between the two sides.
One of the key questions is how close their trading relationship will be once the UK has left.
Mr Rees-Mogg, one of the leading Eurosceptic voices on the Conservative benches, has recently become the chairman of the European Research Group of Tory MPs.
In his speech, he warned against Brexit being treated like a "damage limitation exercise".
People "did not vote for the management of decline", he said.
"They voted for hope and opportunity and politicians must now deliver it."
The North East Somerset MP said some of the "really obvious opportunities" to improve people's lives from Brexit were at risk, if a model similar to the EU's single market and customs union was adopted.
This would leave the UK "divested of even the limited influence we currently have".
Mr Rees-Mogg also said businesses will suffer unless the UK can set its own regulations, independent of the EU.
And he criticised the UK negotiators, who are led by Brexit Secretary David Davis.
"For too long our negotiators seemed to have been cowed by the EU," he argued.
"Their approach seems to be that we must accept what the EU will allow us to do and build from there. This is no way to negotiate and it is no way for this country to behave."
Mr Rees-Mogg told BBC Radio 5live's Brexitcast that his aim in criticising the government's approach to Brexit was to "support the prime minister against naysayers".
Speaking at the World Economic Forum in Davos, Mr Hammond said the UK was not seeking an "off-the-shelf" model to replace its membership of the EU single market and customs union.
The starting point is a position of "high levels of bilateral trade in goods and services," he said.
"So instead of doing what we're normally doing in the trade negotiations - taking two divergent economies with low levels of trade and trying to bring them closer together to enhance that trade - we are taking two completely interconnected and aligned economies with high levels of trade between them, and selectively, moving them, hopefully very modestly, apart.
"And so we should be confident of reaching something much more ambitious than any free trade agreement has ever achieved."
A Cabinet source told the BBC: "The UK is leaving the EU, the sooner Hammond realises that the better. Very modest changes are not what the 52% voted for."
Eurosceptic Tory backbencher Bernard Jenkin told the BBC: "Either the chancellor's been just a little careless in the ambiguity of his remarks or, rather as we suspect, the Treasury's got rather a different agenda. But I think it would be much easier for the prime minister to do her job if everyone just stuck to her script and I think that is what he should do."
He added that while he didn't want one "maybe [the prime minister] needs another reshuffle in order to give herself more ministers who support her policy" but denied he was suggesting Mr Hammond be sacked.
Mr Hammond tweeted:
Former Conservative MP and Scottish secretary Lord Forsyth told the BBC's Question Time that the prime minister "needs to get a grip on the cabinet and the cabinet needs to get behind her".
He added that Mr Hammond seems to be saying "something that's completely at odds with what the prime minister said in her Lancaster House speech."
Downing Street said Theresa May had used major speeches to talk about the "opportunities that Brexit will provide for the country", and that the government was confident of securing these opportunities in the next phase of negotiations.
Asked whether she agreed with Mr Hammond's comments, the spokesman said: "The cabinet has signed up to the vision the PM has set out in her speeches."

European Commission President Jean-Claude Juncker has warned the UK it faces a "very hefty" bill for Brexit.
He promised two years of "tough negotiation", when discussions on leaving terms get under way between the government and the European Union.
Exit will not come "at a discount or at zero cost", he said in a speech to the Belgian Federal Parliament.
Reports suggest the UK could have to pay the EU up to 60 billion euros (£51bn) after Brexit talks start.
Mr Juncker's comments came as the House of Lords held a second day of discussion of the government's European Union (Notification of Withdrawal) Bill, which, if passed into law, will allow Prime Minister Theresa May to trigger Article 50 of the Lisbon Treaty, allowing formal talks with the EU to start.
She is hoping to do this before the end of March, with EU negotiations expected to take up to two years.
Discussions are taking place in Brussels on the size of the bill to be presented to Mrs May when she launches the talks. The amount will cover the UK's share of the cost of projects and programmes it signed up to as a member, as well as pensions for EU officials.
In his speech, Mr Juncker, a former prime minister of Luxembourg, said: "It will be a tough negotiation which will take two years to agree on the exit terms. And to agree on the future architecture of relations between the United Kingdom and the European Union we will need years.
"The British people have to know, they know already, that it will not be at a discount or at zero cost. The British must respect commitments they were involved in making. So the bill will be, to put it a bit crudely, very hefty."
Unpicking 43 years of treaties and agreements covering thousands of different subjects was never going to be a straightforward task.
It is further complicated by the fact that it has never been done before and negotiators will, to some extent, be making it up as they go along.
The post-Brexit trade deal is likely to be the most complex part of the negotiation because it needs the unanimous approval of more than 30 national and regional parliaments across Europe, some of whom may want to hold referendums.
All you need to know about Brexit
He added:  "We need to settle our affairs not with our hearts full of a feeling of hostility, but with the knowledge that the continent owes a lot to the UK. Without Churchill, we would not be here - we mustn't forget that, but we mustn't be naive.
"Our British friends will need to understand that we want to continue to develop European integration."
But an ally of German Chancellor Angela Merkel said it was "not very smart" of the European Commission to ram home the cost of Brexit at this stage.
Stephan Mayer, a CDU member of the German Parliament, told the BBC that while Brexit would be "expensive for both the UK and the EU", much would depend on which EU programmes the UK continued to participate in.
"I am not so happy with this aggressive line," he told BBC Radio 4's Today.
"I am convinced that Germany has a special interest in stable and good relationships with the UK. I fear in a certain way that this harsh pressure, which is put by the European Commission on the UK, is not in Germany's interests."
Mrs May has already said the UK will leave the European single market, but has promised to push for the "freest possible trade" with European countries.
In a speech in January outlining her priorities for Brexit, she warned the EU that to "punish" the UK for leaving would be "an act of calamitous self-harm".
Earlier this month, the House of Commons overwhelmingly backed the EU Bill and the government has said the Lords must not "frustrate" its passage into law.

This is the resignation letter that Lord Adonis says he sent to Downing Street while quitting as the government's infrastructure adviser.
The Right Hon Lord Adonis
House of Lords, London SW1
The Right Hon Theresa May MP
10 Downing Street
London SW129 December 2017
Dear Prime Minister,
The hardest thing in politics is to bring about lasting change for the better, and I believe in co-operation across parties to achieve it.
In this spirit I was glad to accept reappointment last year as Chair of the independent National Infrastructure Commission, when you also reaffirmed your support for HS2, which will help overcome England's north-south divide when it opens in just eight years time. I would like to thank you for your courtesy in our personal dealings.
The Commission has done good work in the past 27 months, thanks to dedicated public servants and commissioners. Sir John Armitt, my deputy chair, and Phil Graham, chief executive, have been brilliant throughout. I am particularly proud of our plans for equipping the UK with world-class 4G and 5G mobile systems; for Crossrail 2 in London and HS3 to link the Northern cities; and for transformational housing growth in the Oxford-Milton Keynes-Cambridge corridor.
I hope these plans are implemented without delay. However, my work at the Commission has become increasingly clouded by disagreement with the Government, and after much consideration I am writing to resign because of fundamental differences which simply cannot be bridged.
The European Union Withdrawal Bill is the worst legislation of my lifetime. It arrives soon in the House of Lords and I feel duty bound to oppose it relentlessly from the Labour benches.
Brexit is a populist and nationalist spasm worthy of Donald Trump. After the narrow referendum vote, a form of associate membership of the EU might have been attempted without rupturing Britain's key trading and political alliances. Instead, by allying with UKIP and the Tory hard right to wrench Britain out of the key economic and political institutions of modern Europe, you are pursuing a course fraught with danger. Even within Ireland, there are set to be barriers between people and trade.
If Brexit happens, taking us back into Europe will become the mission of our children's generation, who will marvel at your acts of destruction.
A responsible government would be leading the British people to stay in Europe while also tackling, with massive vigour, the social and economic problems within Britain which contributed to the Brexit vote. Unfortunately, your policy is the reverse. The Government is hurtling towards the EU's emergency exit with no credible plan for the future of British trade and European co-operation, all the while ignoring - beyond sound bites and inadequate programmes - the crises of housing, education, the NHS, and social and regional inequality which are undermining the fabric of our nation and feeding a populist surge.
What Britain needs in 2018 is a radically reforming government in the tradition of Attlee, working tirelessly to eradicate social problems while strengthening Britain's international alliances. This is a cause I have long advocated, and acted upon in government, and I intend to pursue it with all the energy I can muster.
Britain must be deeply engaged, responsible and consistent as a European power. When in times past we have isolated ourselves from the Continent in the name of "empire" or "sovereignty", we were soon sucked back in. This will inevitably happen again, given our power, trade, democratic values and sheer geography. Putin and the rise of authoritarian nationalism in Poland and Hungry are flashing red lights. As Edmund Burke so wisely wrote, "people will not look forwards to posterity who do not look backwards to their ancestors."
However, I would have been obliged to resign from the Commission at this point anyway because of the Transport Secretary's indefensible decision to bail-out the Stagecoach/Virgin East Coast rail franchise. The bailout will cost taxpayers hundreds of millions of pounds, possibly billions if other loss-making rail companies demand equal treatment. It benefits only the billionaire owners of these companies and their shareholders, while pushing rail fares still higher and threatening national infrastructure investment. It is even more inexcusable given the Brexit squeeze on public spending.
The only rationale I can discern for the bailout is as a cynical political manoeuvre by Chris Grayling, a hard right Brexiteer, to avoid following my 2009 precedent when National Express defaulted on its obligations to the state for the same East Coast franchise because it too had overbid for the contract. I set up a successful public operator to take over East Coast services and banned National Express from bidding for new contracts. The same should have been done in this case. Yet, astonishingly, Stagecoach has not only been bailed out: it remains on the shortlist for the next three rail franchises.
The East Coast affair will inevitably come under close scrutiny by the National Audit Office and the Public Accounts Committee, and I need to be free to set out serious public interest concerns. I hope the PAC calls Sir Richard Branson and Sir Brian Souter to give evidence. I am ready to share troubling evidence with the PAC and other parliamentary committees investigating the bailout.
As you know, I raised these concerns with the Chancellor and the Transport Secretary as soon as the bailout became apparent from the small print of an odd policy statement on 29 November majoring on reversing Beeching rail closures of the 1960s. I received no response from either Minister beyond inappropriate requests to desist.
Brexit is causing a nervous breakdown across Whitehall and conduct unworthy of Her Majesty's Government. I am told, by those of longer experience, that it resembles Suez and the bitter industrial strife of the 1970s, both of which endangered not only national integrity but the authority of the state itself.
You occupy one of the most powerful offices in the history of the world, the heir of Churchill, Attlee and Gladstone. Whatever our differences, I wish you well in guiding our national destiny at this critical time.
Yours sincerely,
(Signed)
ANDREW ADONIS

The European Parliament has backed a motion setting out its position for the Brexit negotiations by 516 to 133.
Although MEPs will not participate directly in the exit talks they will have to vote in favour of the final deal for it to go ahead.
UKIP's Nigel Farage accused MEPs of trying to impose conditions that were "impossible for Britain to comply with" and likened them to the "mafia".
The motion for debate was supported by the two largest groups of MEPs.
It set out general principles at the start of the two year negotiations for the UK to leave the European Union under the Article 50 process.
At a press conference following the vote, Guy Verhofstadt, the European Parliament's Brexit negotiator, said the vote meant that "the UK on the one hand and the [European] Commission on the other hand now know the position of the Parliament, what the red lines are".
He said "the interests of our citizens is our first priority" and called for an early resolution of the status of EU citizens in the UK and UK citizens elsewhere in Europe.
The motion backs a number of positions taken by EU leaders, including the need for a "phased approach" to negotiations.
This would require progress on the terms of Britain's withdrawal, including settling financial commitments, before talks on a future trading relationship can start.
It also backs the call for transparency in the talks, and for the UK to be considered liable for financial commitments that apply after it leaves the EU.
It also says:
During the debate in Strasbourg Manfred Weber, chairman of the largest group of MEPs, the centre-right European People's Party, said: "Cherry-picking will not happen. A state outside the European Union will not have better conditions than a state inside the European Union."
Gianni Pitella, chairman of the European Socialists and Democrats also argued that the UK "can not benefit from the same conditions as members do" and added: "If you leave the house, you still have to pay the bills."
The motion is not binding on European Commission officials but President of the European Commission Jean-Claude Juncker told MEPs: "The role of this parliament is more important than ever. You must scrutinise and validate the final agreement."
He added: "We will of course negotiate in friendship and openness and not in a hostile mood, with a country that has brought so much to our union and will remain close to hearts long after they have left, but this is now the time for reason over emotion.
"What's at stake here are the lives of millions of people. Millions have family or professional links to the United Kingdom."
The EU's chief Brexit negotiator, Michel Barnier, warned that "a disunited union could actually lead to there being no deal".
He added: "The 'no deal' scenario is not the scenario we are looking for. We are looking for success, not against the United Kingdom but with the United Kingdom."
Helga Stevens from the Conservatives and Reformists group, which includes MEPs from the UK's ruling Conservative Party, said Brexit "should not be a nasty breakup" and cautioned MEPs against "making excessive demands in advance" of Brexit talks.
"If we do anything less, history will judge us harshly as being small and petty," she claimed.
But UKIP MEP Mr Farage argued: "Already you've made a series of demands which are not just unreasonable but in some cases clearly impossible for Britain to comply with."
He accused the EU of seeking to impose a bill of £52bn on the UK and likened this to "a form of ransom demand", adding: "What you could have mentioned is we're actually shareholders in this building and other assets and actually you should be making an offer to us that we can't refuse, to go."
When he accused MEPs of behaving like the mafia, the parliament's Italian president, Antonio Tajani, intervened to object. Mr Farage responded:  "I do understand national sensitivities. I'll change it to gangsters."
The former UKIP leader also insisted that Gibraltar should be a "deal breaker" in any negotiations.
Later, Spanish centre-right MEP Esteban Gonzalez Pons accused the UK government of "preventing Scotland staying part of Europe while at the same time they want... Gibraltar to continue to be a tax haven".
At the post-debate press conference, Mr Tajani emphasised the need to uphold the Good Friday Agreement in Northern Ireland and "working for peace".
He also highlighted security co-operation with the UK, saying: "Terrorists know no borders and they do not care about Brexit."

MPs will vote again on how much of a say Parliament should have on Brexit, after another House of Lords defeat for the government.
Peers decided MPs should have to approve whatever the government decided to do next if there was no final agreement with the EU.
Their amendment to the EU (Withdrawal) Bill was backed by 354 votes to 235.
It means the issue is sent back to the House of Commons for a debate on Wednesday.
Leading Tory Eurosceptic Jacob Rees-Mogg accused the Lords of being "cavalier" towards the UK's constitution.
The UK is due to leave the European Union in March 2019. And negotiations have been taking place over the terms of its departure.
But there is an ongoing row about what happens if Parliament votes to reject the final deal reached between the two sides - or if no deal is reached.
One side says Parliament should intervene to prevent the UK from "crashing out" of the EU without a deal - but critics say the prospect of this happening would undermine the UK's negotiating hand.
Last week, Theresa May avoided defeat on the issue - but rebels said they were not happy with the concessions they had been offered in return for not voting against the government.
Now, peers have backed an amendment from former Conservative cabinet minister Lord Hailsham, which goes further than the government's proposals on how much power MPs could get.
The 119 majority was 28 more than the last time peers voted on the so-called "meaningful vote" issue.
Lord Hailsham, who described Brexit as a "national calamity" in his speech, said his amendment represented what had been agreed "in good faith" by the would-be Tory rebels, led by former Attorney General Dominic Grieve, and Downing Street last week.
"It's a matter of honour," he said.
He also said his proposals were in the "national interest", adding: "In order to safeguard our nation's vital interests, in the event that there be no deal on the table, Parliament should have the authority to intervene."
Lord Hailsham described his amendment as "Grieve Two", meaning it was a new version of proposals tabled last week by former Attorney General Dominic Grieve, who wants Parliament to get more of a say over Brexit.
It would apply in three scenarios:
Under these circumstances, the government has said, a minister will make a statement in Parliament, setting out the government's next steps.
The government had offered MPs the chance to vote "on neutral terms" on this statement. But the amendment backed by the Lords on Monday goes further, saying the statement would have to be approved by MPs.
Lord Hailsham also criticised what he called "disgraceful" newspaper attacks on Mr Grieve and said it was "perfectly true" that he had held talks with other parties in drawing up his amendment.
"I make absolutely no apology for that," he said.
"This is the high court of Parliament, and we are not party hacks."
Lord Hailsham's fellow Tory peer Lord True said ministers had already "made a serious attempt to compromise" with the rebels' demands.
"People outside Parliament are getting a little bit tired of the parliamentary games," he said.
"They actually want to know when they're going to get Brexit, when it will be delivered and when it will be done."

Former Liberal Democrat leader Nick Clegg says people should consider joining Labour in an attempt to prevent Brexit from happening.
In his new book, Mr Clegg said it was "a time of national emergency" and he told people worried about Brexit to "make your voice heard".
He also said joining the Conservatives was "another route to make your views felt".
Mr Clegg, the former deputy PM, lost his seat in June's general election.
He has remained an outspoken critic of the UK's departure from the EU, and his new book is called "How to stop Brexit".
In it, he says it "may seem odd" for a former Lib Dem leader to be advocating joining Labour, adding that he himself would not be doing so.
"But if you are someone who has never joined a party, or perhaps has been inclined to join Labour but has never got round to it, or if you are simply someone who recognises that the importance of Brexit is far greater than individual," he writes.
"At a time of national emergency, and for as long as Parliament is dominated by Labour and Conservative MPs, it is undoubtedly true that what happens within the two larger establishment parties is of the greatest importance.
"So if you can't stomach joining the Labour Party, if you are ideologically inclined in a Conservative direction in any event and if you also believe that Brexit is the issue of our times, then joining the Conservatives is another route to make your views felt."

Nicola Sturgeon has warned Theresa May that she is not "bluffing" on the promise of a second independence referendum if Scotland is "driven off a hard Brexit cliff".
Scotland's first minister told the BBC's Andrew Marr she felt the prime minister had "no plan" in terms of her strategy for the UK leaving the EU.
She said she was prepared to compromise and wants Mrs May to do the same.
The UK government has said a special deal for Scotland is unrealistic.
The prime minister said on Sunday morning the government's thinking on Brexit "isn't muddled at all".
In an interview on Sky News, she said her priority was to get the "best possible deal in terms of our trading relationship with the European Union".
Brexit talks with the EU are expected to begin as early as April.
Scottish opposition parties have called for Ms Sturgeon to rule out a second independence referendum.
Voters in Scotland backed the UK staying in the EU by 62% to 38%.
Ms Sturgeon has said she wants the UK to retain membership of the European single market, the so-called soft Brexit option.
She has also indicated a soft Brexit would see the prospect of Scottish independence "put aside" in the short term.
However, in an interview for the Andrew Marr programme, she warned the UK government and Mrs May that "they will be making a big mistake if they think I am in any way bluffing" on the prospect of another Scottish independence referendum.
She said that if the UK opts for leaving the single market then she would "give Scotland the opportunity to decide whether it wants to be driven off a hard Brexit cliff by right-wing Tory Brexiteers or whether it wants to take control of its own future".
Asked if she was looking at a referendum "much quicker" than in five or 10 years' time following a hard Brexit she said: "I would think, yes. But let me not get away from this point, I'm putting to Theresa May a compromise solution."
Ms Sturgeon also told the BBC presenter that discussions with the UK government over the Brexit options had left her "frustrated".
She said: "I don't feel as if I know any more about her (Theresa May's) negotiating objectives than I did six months ago."
Asked if she seriously thinks "there is no plan", the first minister said: "Yes I do".
She added: "I say that with a lot of regret as that puts every part of the UK into a very perilous position."
Nicola Sturgeon has warned she isn't bluffing over a second independence referendum. But she's also been careful to emphasise she is offering a 'compromise' that would take one off the table. For now all options remain in play.
A key influencing decision will be whether Scotland stays in the EU single market, either as part of the UK or in a separate arrangement. Prime Minister Theresa May said today she does not intend to keep bits of membership - instead she wants an ambitious trade deal with Europe.  More details in the next couple of weeks.
But the first minister will also be reluctant to call one unless she's confident she'll win; at the moment polls suggest support for independence has not increased since 2014.
Ms Sturgeon has tried to put the ball in the prime minister's court; asking her will she listen to the views of the Scottish government? If not, Ms Sturgeon thinks Scotland will have to ask itself if it's happy with the decision. Watch this space.
Ms Sturgeon highlighted a meeting at Downing Street in October which also involved the first ministers of Wales and Northern Ireland.
She said: "I'm not exaggerating too much when I say the prime minister sat on the other side of the table at that meeting and said 'Brexit means Brexit' and not a lot more.
"I came out of that meeting more frustrated, after a meeting of that nature, than I have ever been before."
In the interview, the SNP leader also said she accepted "it looks at the moment as though the UK is going to leave the EU".
She called on Theresa May to work towards a "compromise" and "common ground that avoids the worst impacts".
The prime minister has pledged to trigger Article 50 of the Lisbon Treaty - getting leaving talks with the EU under way - by the end of March.
Talks can take up to two years, unless an agreement is reached to prolong the process.
Responding to Ms Sturgeon's comments, Scottish Conservative leader Ruth Davidson said: "This week we've seen Nicola Sturgeon say that she was going to take a referendum off the table, only for her and Alex Salmond to put it back on the table again today.
"The first minister needs to start acting in the interests of all Scots, not simply playing to her nationalist base."
Kezia Dugale, Scottish Labour leader, accused the SNP of sowing "division and uncertainty".
"With a growing crisis in our NHS and a shameful gap between the richest and the rest in our schools, the challenges facing Scotland are too great for the SNP government to be distracted by another referendum," she said.
Scottish Liberal Democrat leader Willie Rennie said Ms Sturgeon was causing "damaging uncertainty".
He added: "She rightly criticises the prime minister for a lack of clarity on Brexit but the first minister is making matters worse with a similar lack of clarity on independence."
The full interview with Nicola Sturgeon was broadcast on The Andrew Marr Show and will be available later on the BBC iPlayer.

The Polish Prime Minister has said Britain will have to continue making financial contributions to the European Union if it wants to enjoy privileged access to the single market.
Mateusz Morawiecki said the EU would take a tough stance on Britain's desire for a comprehensive free trade deal.
He said he wanted a positive relationship, but that costs would be attached.
But a UK minister told me Britain would not agree to that "at the outset".
When I spoke to Mr Morawiecki in Davos I asked him whether Britain would have to pay to get "a good deal".
"I hope so," he told me.
"There has to be some price for full access and to what extent this access is going to be available has to be made dependent on some other contributions, potentially including this financial contribution."
Such a move could be controversial among many Brexit supporters in Britain - a point Mr Morawiecki agreed with.
"Yes, but you cannot have your cake and eat the same cake," he said.
The Polish PM's comments come a few hours after David Davis, the Secretary of State for Exiting the EU, rejected any plans to continue making contributions.
Mr Davis said Britain was a "proud country" and would not pay "some sort of Danegeld".
A Danegeld was a tax levied on the English to pay off Viking raiders.
Mr Morawiecki, who was formerly an adviser to Donald Tusk, the president of the European Council, said he believed there was a small chance that Britain could remain in the EU.
"I still have a little bit of hope that there will be a way of keeping the UK as part of the EU," he said.
"I fully respect the decision from the referendum, but maybe there will be other ways for the UK [to remain] as part of the EU.
"Because I think it's in the interests of the trans-Atlantic community - the pax-Americana, pax-European peace type of model - and for the rest of the world.
"It is extremely important for security, and global trade, and positive trends in the world."
He said if there was no reversal of the referendum - which the UK government has categorically ruled out - then he hoped "the deal between the UK and EU will be as positive for both parties as possible, because I don't want to punish anybody".
I asked the Polish PM whether Britain could have its own bespoke deal, which Theresa May has signalled she wants.
"I would like to indicate two other nations and countries which are [in a different position] - one of them is part of the EEA [the European Economic Area] like Norway, and they do have some financial contribution for the whole of the EU.
"The other one is where we are today, Switzerland, which has a series of bilateral agreements.
"So I think there are examples of how the new agreement can be shaped so that there is a real convergence, a real integration between the UK and the EU, despite Brexit."
Britain is a net contributor to the EU budget and government sources have told me that it is likely the UK will have to pay for special access - possibly via contributions to specific bodies such as for medicines - despite the public position that no payments will be made.
The issue is very important for Poland as it is a net recipient of EU funds and there are concerns that funding could be cut when Britain leaves the EU.
Dr Liam Fox, the International Trade Secretary, said that during the Brexit negotiations both sides would set out - often opposing - positions, and that compromises would have to be reached.
"It sounds to me like the opening shots of a negotiation and there is a long way to go in that," he told me in response to Mr Morawiecki's comments.
"There is no way the UK would agree at the outset to do that.
"What we are looking at is a balance.
"The UK will want access [to the EU] in services, particularly financial services.
"The European Union will want access to Britain's goods market, given that they have got a £82bn surplus with the United Kingdom.
"These things will be netted out over trade agreements.
"In a trade agreement both sides have to give something otherwise you don't get an agreement.
"As we have seen with the TPP [the Trans-Pacific Partnership] agreement, it can sometimes take a few little bumps before people get to the final place.
"So I think we don't assume that any opening positions will be the final positions."

The European Parliament has overwhelmingly approved a non-binding resolution that lays out its views on the Brexit negotiations.
The parliament will have no formal role in shaping the Brexit talks. The negotiations will be led by the European Commission on behalf of the EU's remaining 27 member states. Their draft negotiating guidelines were issued last week.
But the parliament's views still matter because under the Article 50 rules it will get a vote on the final EU-UK "divorce" deal and if it does not like what has been agreed it could demand changes and delay the process.
BBC Reality Check correspondent Chris Morris teases out some of the key sentences from the resolution and explains their significance.
 - A revocation of notification needs to be subject to conditions set by all EU-27, so that it cannot be used as a procedural device or abused in an attempt to improve on the current terms of the United Kingdom's membership;
This is interesting. It implies that the European Parliament thinks the UK can change its mind about Article 50 (whereas the UK government has implied the opposite). The truth is that irrevocability is the subject of legal dispute and, as this is a matter of interpreting a European treaty, the ultimate arbiter would be the European Court of Justice. Either way, the parliament makes clear here that it would not allow the UK to plead for a better deal if it tried to return - even the package of measures offered to David Cameron in February 2016 (remember this?) is now null and void.
 - Reiterates the importance of the withdrawal agreement and any possible transitional arrangement(s) entering into force well before the elections to the European Parliament of May 2019;
In theory the two-year Article 50 negotiating period could be extended if all parties agreed, but no-one really wants that to happen. And this is one of the reasons why the timetable is so tight. If the UK was still part of the European Union in May 2019, it might have to hold elections to elect British MEPs, despite being on the verge of leaving. It would raise all sorts of complications that the European Parliament is determined to avoid.
 - Stresses that the United Kingdom must honour all its legal, financial and budgetary obligations, including commitments under the current multiannual financial framework, falling due up to and after the date of its withdrawal;
Another reminder of the looming fight about settling the accounts (also known as the divorce bill). Parliament insists that the UK must honour all its commitments under the current multiannual financial framework - a kind of long-term budget -  which runs until 2020. Because of the way the EU budget process works, that would mean the UK would have to help pay for things like infrastructure projects in poorer EU countries several years after it had left the Union.
 - States that, whatever the outcome of the negotiations on the future European Union-United Kingdom relationship, they cannot involve any trade-off between internal and external security including defence co-operation, on the one hand and the future economic relationship, on the other hand;
I think this is probably cleared up by now, but the implied link between security co-operation and trade in Theresa May's Article 50 letter raised a few eyebrows elsewhere in the EU. Cooler heads suggested it was there for domestic consumption and the UK government said it was all a misunderstanding. But the parliament is putting down an explicit marker that trade-offs between security and the future economic relationship won't be acceptable.
 - Stresses that any future agreement between the European Union and the United Kingdom is conditional on the UK's continued adherence to the standards provided by international obligations, including human rights and the Union's legislation and policies, in, among others, the field of the environment, climate change, the fight against tax evasion and avoidance, fair competition, trade and social rights, especially safeguards against social dumping;
The resolution suggests that the future relationship could be built upon an agreement under which the UK would have to accept EU standards over a wide range of policy areas from climate change to tax evasion. In some areas that might be exactly what the UK government wants to do anyway, given that the UK has played a leading role in forging those policy positions in the first place. But domestic politics in the UK means any wholesale acceptance of EU policies could be a tough sell.
 - Believes that transitional arrangements ensuring legal certainty and continuity can only be agreed between the European Union and the United Kingdom if they contain the right balance of rights and obligations for both parties and preserve the integrity of the European Union's legal order, with the Court of Justice of the European Union responsible for settling any legal challenges; believes, moreover, that any such arrangements must also be strictly limited both in time - not exceeding three years - and in scope, as they can never be a substitute for European Union membership;
Two important points here. Firstly, the parliament is determined that the jurisdiction of the European Court of Justice would continue to run during any transition period. The draft guidelines produced by the European Council last week made the same point but in less explicit language. If it wants a transition, the UK will have to accept a role for the ECJ. Secondly, the parliament says the transition should last no longer than three years, which is a shorter period than some might think necessary.

Brexit talks will be on a "humongous scale" involving "difficult trade-offs", the UK's ex-EU ambassador says.
Sir Ivan Rogers predicted much of the talks would be "conducted very publicly" with "name-calling" and an "extremely feisty atmosphere".
He added that EU Commission chiefs were saying the UK should pay 40-60bn euros to leave and thought a trade deal could take until the mid-2020s to agree.
Sir Ivan, who had been due to leave his post in October, resigned last month.
In December he attracted criticism from some MPs when his warning to ministers that the European consensus was that a deal might not be done until the early to mid-2020s was revealed by the BBC.
Giving evidence to the Commons European Scrutiny Committee, he said this had come from a briefing he had written for Prime Minister Theresa May in October, based on the views of key figures in the EU and the remaining member states.
He said he did not know how it became public.
The government says it can conclude all separation negotiations, including a new free trade deal, within two years, having given notice of the UK's departure from the EU by the end of March.
Asked about the anticipated timescale, Sir Ivan said a comprehensive free trade agreement such as the one Mrs May was seeking would be the most comprehensive ever negotiated by the EU, and previous agreements have taken "an awful lot of time".
He said he believed an agreement with the UK could be concluded more quickly, but said the Brexit negotiation would be "unprecedentedly large" covering "huge tracts of Whitehall".
"It's a negotiation on the scale that we haven't experienced ever, certainly not since the Second World War."
Sir Ivan said there was a "big financial debate coming up" about the amount to which the UK should be expected to pay as it leaves the EU.
EU commission chief negotiator Michel Barnier and other key figures were "openly" saying the UK's total financial liabilities would be in the order of 40 to 60bn euros, Sir Ivan said, describing this as a "predictably hard line".
From the EU's point of view, UK withdrawal will "explode a bomb" under its seven-year budget, he said.
Sir Ivan told MPs the 27 remaining EU states would spend "an awful lot of time debating with each other" before negotiating with the UK, agreeing a common position.
Asked how confidential the negotiations would be, he said: "I think an awful lot will leak, Brussels is very leaky...stuff will get out, and incessantly in my view."
He added: "Expect an awful lot of this negotiation to be conducted very publicly."
Sir Ivan said that after a "phoney war period" talks "usually end up in a fairly mercantilist fist-fight" before finally resolving themselves in a deal of some sort.
A determination on both sides to make progress would be crucial, he said.
"That involves generating a momentum and generating an atmosphere so that even when we get into name-calling and an extremely feisty atmosphere - and we undoubtedly will in both exit negotiations and future trade and economic negotiations - there is still an atmosphere to proceed and finalise agreement."
He said there was "no doubt" the UK would be able to negotiate free trade deals more quickly than the EU once it leaves, but said it may not have the same "negotiating heft".
Sir Ivan has been replaced by Sir Tim Barrow, a former UK ambassador to Russia.
Giving evidence to a separate Commons committee, International Trade Secretary Liam Fox said the suggestion the UK could face a bill upon leaving the EU was "absurd".
"I find it bizarre because the UK is using a legal power that we have under the Lisbon Treaty, a provision that was freely entered into by all our European partners," he said.
"Why should they then turn round to say that we should pay their costs for a process that everybody equally entered into at the time? So it seems to me an absurd argument."

The EU's chief Brexit negotiator has told the UK the time has come for it to "resolve the contradictions" in its Irish border policy.
Michel Barnier was writing in Ireland's Sunday Independent newspaper ahead of a visit to the country on Monday.
He said there will need to be "substantial progress" on the border issue by the next major meeting of EU leaders.
They are due to assess progress on the border issue at a summit in June.
Last week the Brexit Secretary David Davis suggested the EU was trying to create an "artificial deadline" in June as a negotiating tactic.
The Brexit secretary also rejected reports that the European Commission has completely rejected the UK's plans for avoiding customs checks at the Irish border when the UK leaves the customs union.
October is the presumed deadline for a withdrawal agreement which will give the UK a smooth exit path from the EU.
In March, EU leaders agreed to a 21-month Brexit transition period between March 2019 - when the UK officially leaves - and the end of 2020.

The EU summit on Thursday and Friday will discuss a number of pressing issues, including migration, economics, security and Brexit. But what do different countries want from the Brussels talks and where does Brexit stand in their priorities?
It's tempting to imagine what Angela Merkel and Theresa May might say to one another in a private moment on the margins of the summit.
Both leaders, after all, face dissent and open rebellion from within their own ranks. And both are in a bind over borders.
But that's exactly why it's unlikely that the German chancellor will pay much attention to Brexit this week. She's far too busy trying to realise her long-promised European migration strategy - and saving her own political skin.
Her fragile government hangs precariously in the balance.
And it could fall apart if she can't return home with a solution strong enough to see off the rebellion from her interior minister - and coalition partner - who's threatening to unilaterally impose greater migration controls at the German border.
In such serious times here, the problem of Brexit seems far a less significant issue to preoccupied lawmakers.
But it's not that Germany isn't interested. Industry - in particular the mighty car manufacturing lobby - is beside itself at the thought of a no-deal Brexit.
In recent days, Joachim Lang, the director general of the Federation of German Industries, warned that the UK is "hurtling towards a disorderly Brexit". He added that only by remaining in the customs union and single market can the Irish border question be answered.
Most here want more clarity from Britain about how it perceives its future relationship with the EU, but Mrs May will encounter strong resistance to any proposals that even hint at the reinstatement of a border.
Mrs Merkel, on the other hand, whose experience was shaped by her own early life behind the Iron Curtain in East Germany, now finds herself in an EU openly discussing how and where to strengthen - or even reimpose - Europe's boundaries.
France is going into this summit with two concerns uppermost in its mind.
The first is President Macron's beloved long-term project to tie the eurozone economies more closely together.
The German chancellor seems to have finally agreed in principle to a watered-down version of his plan, including a common budget for the eurozone and extra measures to help countries facing a recession, though the details are still vague. This summit will be a chance to put their ideas to the other EU countries.
The other issue dominating French minds is migration.
President Macron angered Italy earlier this month by saying it was "irresponsible" and "cynical" to refuse a rescue ship carrying illegal migrants. Italy accused France of hypocrisy, in return.
The issue of how to relieve pressure on the front-line states in Europe's migrant crisis is divisive.
In 2015, the former French government promised to take 30,000 refugees from Greece and Italy, but a year later little more than 1,000 had arrived.  And while the French government backs proposals for closed processing centres in front-line states, it does not want to see them on French territory.
With all this occupying French minds, there's little room to devote much attention to Brexit.
France has stuck pretty firmly to the EU line of "no cherry-picking", saying that freedom of goods, services and people cannot be separated.
But there are those in Paris who believe that appetite is growing to find wiggle room on frictionless goods trading, to protect French exporters to the UK. Though there's little indication that Paris will budge on the issue of a "passport" for the City of London and its financial services.
Spain's new prime minister, Pedro Sánchez, has made clear he intends to respect commitments his country has made to the EU and the European project in general.
But with a range of other issues occupying his agenda - particularly increasing numbers of migrants reaching Spanish shores and tensions in Catalonia - Brexit is not a main priority for the socialist premier.
However, he will not be able to ignore the impact the UK's exit could have on Gibraltar, whose British ownership Spain disputes.
At the summit, Mr Sánchez is expected to report on the status of recent negotiations between London and Madrid over Gibraltar's future status. Those talks, due to conclude by October, have focused on the possible shared use of the rock's airport and the exchange of tax information on citizens.
The EU has agreed that Spain can veto a Brexit accord if it is unhappy with the arrangements for Gibraltar.
The summit might offer clues as to whether or not Mr Sánchez intends to continue with the relatively tough line on Gibraltar pursued by the previous Spanish government. Either way, he will want to shore up support from his EU partners on the issue.
To Italy's new populist government, Brexit is a rather distracting sideshow.
It wants to do business with a post-EU UK and it wants to ensure that the rights of Italian citizens living in the UK are protected. But beyond that, Italy's main preoccupation is migration across the Mediterranean.
In this respect, the country has two main objectives: to get EU countries to share the burden of sheltering those who've already reached this continent, and to prevent any more migrants from making the sea journey to Europe.
In particular, Italy wants to get rid of the EU's Dublin Regulation, which calls for migrants to be screened in the first place in which they arrive. Italy believes that this places far too much pressure on front-line countries, including Spain and Greece.
But Italy may face resistance from fellow populist governments in central and eastern Europe, who do not want to take in any more migrants.
Italy's influential Interior Minister, Matteo Salvini, also wants the EU to accept an Italian-Libyan plan announced on 25 June to set up migrant holding centres on Libya's southern borders.
In theory, migrants from Africa would be directed to these centres, and prevented from making the journey across the Mediterranean.
Hungarian Prime Minister Viktor Orban goes into this European summit in confident, but cautious mood.
He feels he's winning the argument on migration, but he knows he hasn't won it yet. Brexit, for him, is already yesterday's story.
His arch-enemy, Angela Merkel, looks wounded. The new government in Rome shares his anti-immigrant rhetoric, as does the government in Vienna.
He can count on Sebastian Kurz, the Austrian Chancellor, to beat the anti-migrant drum for the next six months, as Austria holds the rotating EU presidency.
His allies in Bavaria, Horst Seehofer's CSU, are on the warpath. And the other Visegrad countries are right behind him.
But Mr Orban is playing for time - he sees his real chance after next year's European parliamentary elections, when he counts on a much bigger role for populist parties like his own, and populist leaders like himself, in the running of the European Union.
In the meantime, he still has to face annoying distractions, like criticism in the European Parliament for his crackdown on human rights groups.
He'll be hoping the summit is over as quickly as possible, so he can get back to watching the football. He hasn't missed a match yet, he told Hungarian radio.

"It's all kicking off," an MP texts tonight.
It's not surprising given what's at stake, and that we are seven days away from a critical EU summit. But it's not a drama that can easily be dismissed.
The government's backers the DUP are threatening to pull support if the PM doesn't bend to their position on Brexit. Don't be in any doubt, that could in theory mean the government collapsing because they can't get anything done.
Rather than pulling back from the threat, the DUP will in the next 24 hours be trying to turn the pressure up even further.
And to make the threats real the small Northern Irish party has already tonight decided not to back the government in a vote in the Commons - a reminder that the  government's vulnerability in the Commons is real, it's not some theoretical threat.
It's a warning - not an obscure abstention on a little-noticed piece of legislation. And remember, remember December. It was the DUP (and some very strong Brexiteer voices too) who sank the prime minister's original Brussels agreement, humiliating her before she snatched victory from the jaws of defeat a few days later.
As we enter the next phase of this drama, catch up on the last big denouement here.
In Brussels, contrary to some reports, there has not been some sudden breakthrough on the clashes across the negotiating table.
Well-placed sources on both sides tell me that while the "show is on the road", and officials have been "working well" in the last three days, neither Team Barnier nor Team Robbins are buckling and bending.
So, it follows, neither Team Barnier nor Team Robbins can claim victory, and more importantly, neither Team Barnier nor Team Robbins can say at this moment with complete confidence that the progress they hope for to allow Theresa May to move closer to a Brexit deal has been achieved.
That's not of course to say that it won't or can't still happen.
There is a significant chance that by Monday Dominic Raab and Michel Barnier will be side by side at the podium gleefully reporting the progress their worker bees have been able to make - a springboard for a successful summit a week tonight.  But they are not there yet.
In cabinet too there are plenty of reservations too about the prime minister's direction of travel as well as a loyal brigade.
The jokingly named "Chequers Defence Committee", a group of the most senior ministers and those whose departments are most affected by Brexit, are being called into Number 10 late tomorrow afternoon.
But sources suggest this is not to make any kind of decision about the Brexit deal. It's to keep them broadly on board, and to avoid accusations further down the line that Number 10 has bounced ministers into signing up.
One of the profound criticisms of the prime minister has often been that she and her officials are intensely secretive, and don't seek genuine buy-in from colleagues.
It's not mad to argue that with such divisions in her party that's been the way to survive.
But it has infuriated some of her colleagues. And it also means that objections and concerns have developed rather than been fully argued out and discussed.  It's also why the finger often gets pointed at the officials leading the talks.
Brexiteer knives have been out for Olly Robbins, the lead negotiator, for a long time now. It often seems the Brexit deal is being struck by him and Number 10 with the Brexit department looped in, rather than by the government as a whole.
But as one well-placed source acidly suggests: "Robbins does not get the SW1 politics of this - but it's ultimately her fault for letting a civil service man do a woman's political job."
There are of course plenty of loyalists - plenty of MPs and ministers who think the PM is faced with an absolute nightmare, in office but not in power with no majority, and simply trying to do a sensible best.
But there are concerned Brexiteer ministers, worried former Remainer ministers and as we've discussed many times here, widespread discontent on the Tory backbenches on all sides at the prime minister's hoped-for compromise.
Even some of Theresa May's most ardent backers worry that there's a disconnect that might go badly wrong.
While the government believes they probably do have the numbers when it gets to a final vote as I wrote here, I've heard from former Remainers as well as Brexiteers this week who say the same - "I just can't see how they get anything through."
It was of course always extremely likely that in the closing weeks of this negotiation the situation would be extremely febrile and it would all be "kicking off".
The second last episode in any box set is almost always when the heroes teeter on the edge of disaster before miraculously coming back from the brink.
In a couple of months this might seem like froth. But tonight the prime minister's vital backers are threatening to pull stumps; her cabinet is yet to be convinced; her backbenches certainly can't be relied on and the talks themselves are not sorted.
It certainly is all kicking off, and the government may well get hurt.

The woman who started the record-breaking anti-Brexit petition says she is "shaking like a leaf" after receiving three death threats by phone.
Margaret Georgiadou, 77, began the Revoke Article 50 petition, which had topped four million signatures by Saturday morning.
She said she was "totally amazed" it had become the most popular petition submitted to the Parliament website.
But Mrs Georgiadou said the "horrible" phone calls left her scared and angry.
The retired lecturer says she has also received abuse via her Facebook account.
She said: "I feel terrible, I feel angry with myself because I thought I was tougher than that. But I was scared."
"I haven't even told my husband because he is very old and he would become hysterical."
Mrs Georgiadou said she created the petition to stop people "moaning" about how awful they thought Brexit was going to be.
It has broken the record for the biggest petition on the Parliament's website, previously held by another Brexit-related petition from 2016.
Mrs Georgiadou said she wanted to get as many people as possible to sign it - but she wasn't hoping for a government response.
"Democracy is ruled by society for society, not the majority for the majority," she said.
"I want it to prove it is no longer the will of the people. It was three years ago but the government has become infamous for changing their mind - so why can't the people?
"People should ask themselves, who is it that wants Brexit? It will help Putin, it will help Trump… but will it help us? I doubt it," she continued.
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Since the success of her petition, Mrs Georgiadou has faced criticism over posts she allegedly made on social media, using threatening language about the prime minister. She said she had no memory of the posts.
She said:  "It must have been a cut and paste job. The dates were all wrong."
"My friends thought it was funny. They have made photos of me trying to hold up a rifle with my zimmer-frame... I don't own a zimmer-frame by the way - or a rifle."
Mrs Georgiadou says she cannot attend the march for another EU referendum in London on Saturday but would welcome tributes from the demonstrators.
"I want them to sing a song for me, 'March on, march on, with hope in your heart and you'll never walk alone'."

Brexit negotiations "have been difficult" and "no solution has been identified" to the Irish backstop, the European Commission has said.
It comes after the latest talks between UK ministers and EU Brexit negotiator Michel Barnier in Brussels.
Commission spokesman Margaritis Schinas said the talks had taken place in a "constructive atmosphere" but there had been no breakthrough.
The UK is pushing for legally-binding changes to the EU deal.
Mr Schinas was speaking after Mr Barnier briefed the European Commission's weekly meeting on the state of Brexit talks.
Speaking after talks with Mr Barnier, the UK's Attorney General Geoffrey Cox said: "Both sides have exchanged robust, strong views. We're now facing the real discussions. Talks will be resuming soon."
He added: "We're into the meat of the matter, we've put forward very reasonable proposals."
Downing Street echoed Mr Barnier's characterisation of the talks as "difficult", but said the negotiations were "ongoing".
"The EU continues to say that it wants this to be resolved and that it wants the UK to leave with a deal. Parliament has been clear that for this to happen, we require legally-binding changes which mean that the UK can't be trapped in the backstop indefinitely," said the PM's official spokesman.
"That is what we will continue to pursue."
The backstop is an insurance policy - designed to avoid a hard border "under all circumstances" - between Northern Ireland and the Irish Republic.
Prime Minister Theresa May is pinning her hopes on getting changes to it that will prevent the UK from being tied to EU customs rules if no permanent trade deal is agreed after Brexit.
She believes this would be enough to get MPs - who last month rejected her deal by an historic margin - to back her deal in a vote she has promised on or before 12 March.
But the EU has consistently refused to rewrite the deal it has struck with Mrs May, which is meant to ensure an orderly departure from the bloc on 29 March and pave the way for trade talks.
And Mr Barnier repeated that message to EU leaders, according to Mr Schinas.
"Discussions have been difficult and no solution has been identified to that is consistent with the withdrawal agreement, including the Northern Ireland protocol which, as you know, will not be reopened," he said at a press conference in Brussels.
BBC Brussels reporter Adam Fleming explained that EU sources said the UK side couldn't guarantee that whatever might end up being agreed in Brussels would even get through Parliament.
Mrs May is also hoping to attract votes from Labour MPs in Leave-voting areas of the UK, as she battles to get her deal through the Commons.
She is promising MPs a vote on any changes to workers' rights after Brexit.
No 10 said Parliament would be given a say over whether to adopt any new protections introduced on the continent and to stay aligned with EU standards.
Labour MPs have been seeking assurances the UK will not fall behind EU standards after Brexit.
But trade unions said the MPs should not be "taken in by blatant window dressing" and the assurances on workers' rights were "not worth the paper they are written on".
Meanwhile, Labour leader Jeremy Corbyn has met Conservative MPs who back a close, Norway-style relationship with the EU after Brexit.
He discussed the idea of a "Common Market 2.0" trade-focused model with former ministers Nick Boles and Sir Oliver Letwin.
Mr Boles said the goal was to reach a cross-party compromise to ensure the UK left the EU but in a manner which protected its economic interests.
The Labour spokesman said the meeting was to "discuss how to achieve a deal that would be good for jobs and could bring Leave and Remain voters together".
The meeting comes after Mr Corbyn and the main business organisations - the CBI, the Institute of Directors, the Federation of Small Businesses, the British Chambers of Commerce and Make UK - met on Tuesday to discuss Labour's Brexit plan based on a customs union with the EU.

There have been "fruitful" discussions on Irish issues at the Brexit talks, the EU's chief negotiator has said.
Michel Barnier also said there had been "genuine progress' on the Common Travel Area (CTA).
The CTA is a UK-Ireland arrangement allowing free movement of UK and Irish citizens between the Republic of Ireland, NI and the rest of the UK.
Mr Barnier was speaking in Brussels at the end of the third week of Brexit negotiations with the UK.
There has been slow progress on other major issues, including the size of the so-called Brexit bill the UK will have to pay.
Mr Barnier said negotiations were still "quite far" away from being in a position to begin talks on future trade arrangements.
UK Brexit secretary David Davis said he had a duty to tax payers to "rigorously interrogate" the EU's position on the bill.
But Mr Davis said the talks had been "constructive" overall.
He said there was a "high degree of convergence" on the CTA, and recognition of the need for joint work on other cross border issues.
The Brexit secretary urged the EU to be "more imaginative and flexible" in its approach.
Chancellor of the Exchequer Philip Hammond was in Dublin on Thursday, where he met the Irish Foreign Minister, Simon Coveney.
Mr Coveney said he had "urged" the chancellor to "listen to those who stand to be most negatively impacted by Brexit across these islands".
He said he had emphasised that the UK remaining in the Customs Union and the Single Market was the best way to avoid a hard border.
In article for the Irish Times, Mr Hammond said the UK government was determined "to avoid any physical infrastructure" along either side of the border.
"Our economies are already closely entwined. Our businesses operate across the land and sea borders, and so do our people," he wrote.

The government has distanced itself from a page of Brexit notes caught on camera in Westminster.
The handwritten notes, carried by an aide to Conservative MP Mark Field, included "what's the model? Have your cake and eat it" and "unlikely" in reference to the EU single market.
They were photographed after Mr Field and his aide left a meeting with the Brexit department at 9 Downing Street.
The government said the notes did not reflect its Brexit position.
"These individual notes do not belong to a government official or a special adviser. They do not reflect the government's position in relation to Brexit negotiations," a spokesman said.
The notes, held by Mr Field's chief of staff Julia Dockerill, were captured on a long-lens camera by photographer Steve Back.
"Difficult on article 50 implementation - Barnier wants to see what deal looks like first," they note, in an apparent reference to the lead EU negotiator Michel Barnier.
"Got to be done in parallel - 20 odd negotiations. Keep the two years. Won't provide more detail. We think it's unlikely we'll be offered single market," they also say.
Among the reaction from other EU members, Luxembourg PM Xavier Bettel said of the UK stance: "They want to have their cake, eat it, and get a smile from the baker, but not the other things... there are European values which cannot be separated. No cherry-picking."
The BBC's assistant political editor Norman Smith says the government's response, playing down the picture's significance, underlines just how "awkward" it is, because it does seem to be of a view held "within" the Brexit department.
"The real damage is that phrase 'what is the model? Have cake and eat it.' The damage is the way that will be read by other EU countries," he says.
It is not known who Mr Field - a vice-chairman of the Conservative Party and MP for the Cities of London and Westminster - was meeting, or if the page of scribbled notes being carried by his aide is definitely an account of talks at the department handling Britain's departure from the EU.
The notes appear to suggest that a transitional arrangement - which would allow the UK continued access to the single market after Brexit while it negotiates a new trade deal - is also unlikely.
"Transitional - loath to do it. Whitehall will hold onto it. We need to bring an end to negotiations," the paper reads.
The picture is enough to give Downing Street indigestion. But as the last shenanigans over a memo suggested, unless and until Number 10 is willing to share more details of their plans, or at least be clearer about the broad answers to the questions, every scrap or information will be pored over by journalists and interested parties, eager, if not downright desperate, for more information.
If there is a vacuum, others will fill it. Downing Street is well aware of this. And some of the Number 10 team don't think it's a sustainable situation. But in the absence of a traditionally functioning opposition, and look at today's polls which suggest a stonking lead for the Tories, this lack of information does not, at least, appear to be doing much wider harm.
The document also says it is "unlikely" the UK will remain in the single market, and that a transitional arrangement, immediately after Brexit, will not happen either.
It says a deal on manufacturing should be "relatively straightforward", but one on services will be "harder" to achieve.
And in what appears to be a reference to the negotiating team the government will encounter in Brussels, the document says: "Very French. Need fair process guaranteed."
The government has refused to reveal details of its Brexit negotiation strategy in advance, saying it will not offer a "running commentary".
Debate has focused on the level of access the UK could secure to the single market, and whether this would come at the price of greater immigration controls.
For Labour, shadow Brexit secretary Keir Starmer called for the government "to come clean, to end this unnecessary uncertainty and publish a clear plan for Brexit".
"These disclosures are significant because they suggest that the government is not even going to fight for the single market or customs union in the negotiations. If that is the case, there are huge implications for the economy, for businesses and for jobs in the UK," he said.
Lib Dem leader Tim Farron said: "If this is a strategy it is incoherent. We can't have our cake and eat it and there is no certainty on the single market. This picture shows the government doesn't have a plan or even a clue."

Theresa May has rejected claims she does not believe in Brexit - and insisted she would make a success of it "regardless of the outcome" of talks.
She told the BBC's Andrew Marr Show her plan for post-Brexit trade with the EU was not dead, despite it having been rejected by EU leaders.
And she urged the Tory party - in Birmingham for their annual conference - to "come together" and back it.
Boris Johnson has called her so-called Chequers plan "deranged".
In his latest broadside against her Brexit strategy, the former foreign secretary suggested he might be able to strike a better deal than her with Brussels.
He told the Sunday Times : "Unlike the prime minister, I fought for this, I believe in it, I think it's the right thing for our country and I think that what is happening now is, alas, not what people were promised in 2016."
Mr Johnson also set out domestic policy ideas, including building a bridge between Britain and Ireland and putting the HS2 scheme on hold to focus on a rail link in northern England.
Mrs May, who campaigned for Remain in the 2016 EU referendum, hit back at Mr Johnson in her Andrew Marr interview.
She said: "I do believe in Brexit. Crucially, I believe in delivering Brexit in a way that respects the vote and delivers on the vote of the British people while also protecting our union, protecting jobs and ensuring we make a success of Brexit for the future.
"That's why I want us to get a really good free trade deal with the European Union, which is what lies at the heart of the Chequers plan."
But she also said she was prepared for a "no deal" scenario, saying: "We will make a success of Brexit, regardless of the outcome of the negotiations."
The Labour Party has said it will back Mrs May in Parliament if she agrees to their plan for a customs union with the EU and a Brexit deal that guarantees workers' rights and protects jobs.
Mrs May said: "My message to the Labour Party is that they should stop playing politics with Brexit and start acting in the national interest.
"My message to my party is let's come together and get the best deal for Britain."
EU leaders have rejected her Chequers plan because they believe it would undermine the single market by allowing the UK to "cherry pick" bits of EU law it liked and ditch the rest.
Mrs May said: "We think we are putting forward a proposal that will maintain the integrity of the single market."
She said she wanted a more detailed response from the EU on their objections.
Later on Sunday, Foreign Secretary Jeremy Hunt hit back at the EU's negotiation stance in his speech to the party conference.
He said the EU seemed to want to "punish" the UK for leaving, and added: "If you turn the EU club into a prison, the desire to get out of it won't diminish, it will grow and we won't be the only prisoner that will want to escape."
Mr Hunt also addressed EU leaders directly, saying: "If you reject the hand of friendship offered by our prime minister, you turn your back on the partnership that has given Europe more security, more freedom, more prosperity, more opportunities than ever before in history."
In the main conference hall, pro-Brexit former CBI chief Sir Digby Jones gave a watching Mrs May a boost with a speech hailing her for standing up to the EU "bully boys" and attacking Mr Johnson as an "irrelevance".
By Chris Mason, BBC political correspondent, in Birmingham
Just like the Labour conference last week, the Conservatives are keen to show us they have plenty of songs on their playlist.
But just like the Labour conference last week, one record is louder than all the others and seems jammed on repeat: Brexit.
Autumn guarantees two things: leaves falling off trees and Conservative conferences in which there is a series of deftly choreographed Johnsonian interventions, before and during the main event.
Forty-eight hours on from his 4,000 or so words for the Daily Telegraph, one word from Mr Johnson is sufficient to grab a headline or two today: "deranged".
The big question of the next few days, beyond the Brexit noise: does the PM offer any indication, however vague, of the possibility of her shifting on her much criticised Brexit plan?
But former Brexit Secretary David Davis, who like Mr Johnson quit the cabinet over Mrs May's Brexit proposals, told Sky News the Chequers plan "will die" because "it's just wrong".
He said he expected a free trade deal to be struck along the lines of a Canada-style agreement, adding that "we are going to have a very scary few months" as talks with the EU entered their final stages, but that was "normal".
On the Andrew Marr Show, Mrs May also defended the "hostile environment" immigration policies she introduced as home secretary,  which led to people from the so-called Windrush generation losing their jobs, welfare benefits and right to remain in the UK.
She apologised for the fact that many long-standing UK residents of Caribbean origin had been caught by her Immigration Act, but declined to apologise for the policy itself.
Mrs May wants to use the Conservative conference to focus on domestic issues as well as Brexit, after Labour unveiled a string of new policies at its conference last week.
She has announced plans to tackle a big increase in rough sleeping, to be funded by a tax on foreign-owned homes.
The Prime Minister also revealed plans for a Festival of Great Britain and Northern Ireland to showcase the nation in January 2022 - months before the next scheduled general election.
And Health Secretary Matt Hancock said health officials would produce guidelines on the amount of time young people should spend on social media.

British passports will change from burgundy to blue after Britain leaves the EU, the Home Office has said.
Immigration Minister Brandon Lewis said he was delighted to return to the "iconic" blue and gold design which came into use almost 100 years ago.
The new passports will be issued to those renewing or applying for a passport from October 2019.
Burgundy passports were first issued in 1988. The EU has never compelled the UK to change the colour of its passport.
Former UKIP leader Nigel Farage responded to the announcement by tweeting "Happy Brexmas!"
He added: "In the 2016 referendum, we wanted our passports back. Now we've got them back!"
But Labour MP Mary Creagh tweeted: "No-one under 45 will have owned a blue passport, and most will think they're not worth £50 billion and crashing the economy."
Mr Lewis told BBC Radio 4's Today programme he knew many Remain voters who still had an "attachment" and "speak fondly" of the blue passport.
By Dominic Casciani, home affairs correspondent
Did Brussels force the UK to change the colour of its passport? No.
The European Union has never had the power to force the UK to change the colour of the British passport.
Dumping the blue for burgundy was a decision taken by the UK in the 1980s after the then EEC (European Economic Community) member states tried to harmonise designs to make life easier for travellers and border officials.
So this wasn't a decision forced on the UK by Brussels Eurocrats. Ministers could have ignored it.
Croatia retained its blue passport after it joined the EU in 2013.
In a similar vein, the EU has never had the power to order the UK to remove references to Her Majesty The Queen from the passport. It is still a British document, but with added EU wording to guarantee freedom of movement.
The only legal requirement to harmonise EU passports related to security standards, part of a global governmental effort to combat forgery.
If the EU wanted passports to change in any other way, the plans would need each government to agree.
Tory MP Andrew Rosindell, who campaigned to bring back the blue passport, tweeted: "A great Christmas present for those who care about our national identity - the fanatical Remainers hate it, but the restoration of our own British passport is a powerful symbol that Britain is Back!"
However, many other people have mocked the announcement on social media.
Simon Blackwell, a comedy writer, said: "Why do we need any colour passport? We should just be able to shout, "British! Less of your nonsense!" and stroll straight through."
According to the Passport Index, 76 countries have blue passports, including a number of former colonial and Commonwealth countries, such as Australia, the United States, Canada, India and Hong Kong.
Several Caribbean countries also have blue passports, including Jamaica, Antigua and Barbuda, Barbados and St Vincent and the Grenadines.
In Europe, people from Iceland and Bosnia and Herzegovina both carry blue passports, while it is also a popular colour in central and south America - Argentina, Brazil, Costa Rica, El Salvador, Uruguay and Venezuela are among those that have them.
Others include Israel, Iraq, Syria and North Korea.
Stig Abell, editor of the Times Literary Supplement, tweeted: "I've just spent the last 10 minutes screaming 'Take that you burgundy symbol of EU oppression' at my passport.
"It just stares insolently back, as if it is an inanimate and merely functional object and its colour doesn't matter."
The new passports will also have updated security features to protect against fraud, Mr Lewis said.
The Home Office said there was no need for British passport holders to do anything ahead of their current passport renewal date, adding that the changes would be introduced in phases.
When the UK leaves the EU in March 2019, burgundy passports will continue to be issued but with no reference to the European Union.
The blue passports will be issued later the same year, after a new contract for their production is negotiated.
"Leaving the EU gives us a unique opportunity to restore our national identity and forge a new path for ourselves in the world", Mr Lewis said.

The President of the European Council, Donald Tusk, has told the Taoiseach, Leo Varadkar, that Ireland's interests come first in the Brexit negotiations.
Speaking in Dublin, Mr Tusk said nothing must be done to risk the peace process or the Good Friday Agreement.
He said every EU leader he has met has expressed support for Ireland's position.
He called on the British government to produce a "realistic solution" to avoid a hard border on the island of Ireland.
Mr Tusk said: "If in London someone assumes that the negotiations will deal with other issues first before moving to the Irish issue, my response would be 'Ireland First'."
Responding to Theresa May's criticism of the draft Withdrawal Agreement which the Commission published on 28 February, Mr Tusk said: "We also have to be clear that any backsliding on the commitment made so far would create the risk to further progress in Brexit negotiations."
"Since my last visit to Dublin I have spoken to virtually every EU leader and everyone without exception declared... that among their priorities are protecting the peace process and avoiding a hard border. The EU stands by Ireland."
Mr Tusk began his comments with some light-hearted weather references saying: "I may be from the east but I am not a beast".
But the tone quickly became more serious as he reaffirmed the EU position on the negotiations:  "We also expect the UK to provide a specific and realistic solution to avoid a hard border. As long as the UK doesn't present such a solution, it is very difficult to imagine substantial progress in Brexit negotiations."
Mr Varadkar told the news conference: "I've always said that my preference is to avoid a hard border through a wider future relationship between the United Kingdom of Great Britain and Northern Ireland and the European Union.
"We're committed to playing our part in exploring this option, or alternative specific solutions, in a way that respects the structure of these negotiations and that will of course require further detailed progress to be put forward by the UK government.
"However we must have certainty that if a better option proves unachievable, the backstop of maintaining full alignment of Northern Ireland with those rules of the single market and customs union that apply in order to protect north-south co-operation and avoid a hard border."
Mr Tusk also referred to a recent speech by Chancellor of the Exchequer, Philip Hammond in which he called for financial services to be included in a future trade deal.
The EC president said: "Services are about common rules, common supervision and common enforcement, to ensure a level playing field, to ensure the integrity of the single market and ultimately also to ensure financial stability.
"This is why we cannot offer the same in services as we can offer in goods.  It's also why FTAs (free trade agreements) don't have detailed rules for financial services.
"We should all be clear that, also when it comes to financial services, life will be different after Brexit."
Responding to Mr Hammond's assertion that it was in the interest of both Britain and EU to ensure that UK-based financial services companies had easy access to the single market, Mr Tusk said: "I fully respect the Chancellor's competence in defining what is in the UK's interest. He must allow us to define what is in the EU's interest."
Democratic Unionist MEP Diane Dodds said Mr Tusk's comments suggest the EU will again hold up the trade talks if the December fall-back option of alignment is not legally translated.
"Far from putting 'Ireland first' this will generate further frustration among Republic of Ireland businesses dependent on access to their primary marketplace in the UK," she said.
"These include Irish agri-food firms which export around 40% of their produce to Great Britain and Northern Ireland."
SDLP leader Colum Eastwood said Mr Tusk's comments showed that "the EU is not messing about".
"It is crystal clear that the EU's commitment to protecting the interests of the island of Ireland is immovable," he said.

A majority of police forces in England and Wales saw record levels of hate crimes in the first full three months following the EU referendum, according to new analysis.
More than 14,000 hate crimes were recorded between July and September.
In 10 forces the number of suspected hate crimes increased by more than 50%, compared to the previous three months.
Police say their own monitoring suggests incidents have levelled out after the summer's spike.
Last October the Home Office published provisional figures which suggested the number of hate crimes in July 2016 had been 41% higher than 12 months earlier.
Those 5,468 reports indicated there had been a spike in reports - supporting anecdotal evidence across the country of an increased number of threatening, violent or abusive incidents.
The fresh data compiled by the Press Association comes from official statistics which include detailed figures for five core crimes which are deemed to be racially or religiously aggravated, ranging from assaults through to criminal damage.
In the three months to September 2016, 33 of the 44 forces in England and Wales saw their highest levels of hate crimes since comparable records began in 2012.
Dorset and Nottinghamshire saw the highest percentage increases in reports - 100% and 75% respectively - compared to the levels seen between March and the end of June. That previous period had included the referendum campaign itself and the week immediately after the vote.
The Metropolitan Police in London recorded the highest number of hates crimes, with 3,356 in that period, while Greater Manchester and West Yorkshire Police recorded 1,033 and 1,013 respectively.
South Yorkshire, Gloucestershire, Surrey and City of London Police posted falls in hate crime.
Assistant Chief Constable Mark Hamilton, the National Police Chiefs' Council's lead for hate crime, said: "We know that national and global events have the potential to trigger short-terms rises in hate crime and we saw this following the EU referendum last year.
"Police forces took a robust approach to these crimes and reporting returned to previously seen levels.
"These numbers are still far too high.  We have increased the central reporting and monitoring functions to enable us to recognise spikes earlier. This will be used to assess any threats that may arise and inform local police activity."
Analysis by Dominic Casciani, BBC home affairs correspondent
While the overall figure from this analysis comes to 14,300 hate crimes in three months, it can't confidently be claimed as a quarterly national record across the UK because of the complicated way that hate crimes are counted.
There's no doubt there was a spike after the Brexit vote, but the long-term picture won't become clear for months. And if 2016 turns out to be a record year, there still needs to be some caution about what the figures mean.
Sexual offences rose in recent years thanks to more people coming forward to report what had happened to them.
If there is a long-term rise in hate crime recorded by police, it may simply reflect that victims have more confidence that it is worth speaking to the police.
But David Isaac, chairman of the Equality and Human Rights Commission, warned that many people remained anxious.
"It must be sensible to prepare for any possible spikes during the Brexit process," he said.
"The triggering of Article 50 is the next major milestone and we must do all we can to discourage hate attacks and to support people who feel at risk."
Fizza Qureshi of Migrants' Rights Network, a campaign group that runs an online service encouraging people to report hate crimes  and have them recorded on a real-time map, said: "The experience of thousands of people in the UK of discrimination, hostility and at times violence is invisible to many people in Britain - but today's figures lay it bare for all to see."

Prime Minister Theresa May has been forced to quit. Parliament is deadlocked. Both the Conservative and Labour parties are deeply divided and deeply unpopular.
What's more, with days to go before there is a new occupant of No 10, no-one has identified a clear route to an agreement that will avoid an outcome pretty much everyone says they want to avoid - a costly and disruptive no-deal Brexit. So, how did the UK end up here?
For the past few months, the BBC's Panorama team has spoken to those with first-hand knowledge of the negotiations - in Brussels, Paris and Dublin as well as Westminster. We've interviewed at length, on and off the record, the men and women who tried and failed to make a Brexit deal that both the UK and the EU could agree to.
This is an account of 10 crucial mistakes, mishaps and misunderstandings that might explain why we haven't left yet.
George Bridges was a new minister in the Brexit department created from scratch in 2016 when Theresa May became prime minister - a job she only got because the UK voted to leave the EU.
At least Bridges had an office. Secretary of State David Davis's political advisers had to share a cupboard, while the department's top official had to change his office three times in one day. It was chaos.
Lord Bridges, who was a junior minister, assumed that the thinking about Brexit must be taking place somewhere else:
"I was very much under the view that there would be somewhere in No 10 a very small, very secret group, putting together an almighty chart, a big plan of how we were going to negotiate and crucially what our overall objectives were. So, the prime minister - rather like a Bond villain - would be sitting with her white cat on her lap with this big plan behind her. I'd love to say that that room existed. I never found it."
He wasn't the only one. In Brussels, top EU officials were waiting to see what the UK would propose.
"We thought they are so brilliant there will be, in some vault somewhere in Westminster, a Harry Potter type book with all the tricks and all the things in it to do."
Frans Timmermans, first vice president of the European Commission, was shocked by what he saw and heard. Or rather what he didn't:
"I thought, 'Oh my God, they haven't got a plan…they haven't got a plan… it's like Lance Corporal Jones'. It was, 'Don't panic, don't panic,' running around like idiots."
The truth is there was no plan for Brexit when the UK voted to leave. David Cameron had no Plan B when he called the EU referendum. One senior official says he stopped civil servants preparing one as he was fearful it might leak.
The main Leave campaign, led by Boris Johnson and Michael Gove, had decided not to produce a Plan A. They knew the choices that would have to be made would split their coalition of support.
Theresa May came to office without a plan. Indeed, she barely mentioned Brexit in her speech in Downing Street.
Speaking to the BBC, former French President Francois Hollande says he told his fellow EU leaders straight after the referendum that the UK would have to pay a price:
"Brexit might lead to a slippery slope where others, and particularly those under the sway of populists, might decide to follow what the British have just been doing."
EU leaders sensed that populism was on the march. Brexit was followed by the election of Donald Trump.
When the new US president called the other President Donald - Donald Tusk, the president of the European Council - he asked a question with a hint of menace: "Who's next?"
With elections due in France and the Netherlands in 2017, this was no mere taunt. The leader of the French National Front, Marine Le Pen, was campaigning for "Frexit". Polls suggested victory was likely for the Dutch far right leader Geert Wilders. Hungary, Austria and Italy were already governed by politicians who were highly critical of the EU.
There were tears in the office of Jean-Claude Juncker, the president of the European Commission, when he and his officials heard that the UK had voted to leave.
Juncker's right hand man was a formidable German lawyer called Martin Selmayr, thought by many to be the most important man in Brussels. Giving his first British broadcast interview to Panorama, he says:
"I think the most important thing at this moment in time was to preserve the unity of the other 27 member states - to make sure that in the process that followed, all 27 saw eye to eye …[and] to use this moment not to further weaken the [European] Union, not the beginning of the end, but the start of a new beginning for the European project," says Selmayr.
When Selmayr met the British minister he knew best, David Lidington,  who'd been Minister for Europe for many years and who would go on to become Theresa May's de facto deputy - he spelt out what this would mean. Lidington recalls this conversation:
"He said to me, 'Look David, there's not going to be the traditional EU late into the night, into the wee small hours, horse trading on this. It'll be the Commission that your side talks to. We are not going to give your prime minister the chance to try and pick us off."
The UK was no longer to be treated like a member of the club, in which it could seek to build alliances and divide and rule the 27 countries still inside. It would be treated as if it had already left.
Negotiations would take place not with representatives of every country but with a team led by one man - a suave silver-haired Frenchman called Michel Barnier. In his first British broadcast interview since the negotiations began, he told Panorama:
"Everybody will have to pay a price - EU and UK - because there is no added value to Brexit. Brexit is a negative negotiation. It is a lose-lose game for everybody."
Philip Hammond didn't like what he was hearing. Theresa May was delivering her first speech as prime minister to the Conservative Party Conference in 2016, and her new chancellor of the Exchequer was sitting in the audience.
"I was trying to keep my face dead straight, conscious that there were cameras on me," he says.
May began by saying that "Brexit means Brexit and we're going to make a success of it". That came as no surprise to Hammond. He'd heard her use the phrase many times before.
But then the prime minister continued: "Our laws will be made not in Brussels but in Westminster. The authority of EU law in Britain will end." That meant that the UK would have to leave the single market. It could not stay as close as possible to the EU economically - like Norway or Switzerland.
Hammond says that he had not been consulted about the speech or the policy:
"I didn't know. I think the prime minister felt that as a former remainer she needed to demonstrate her credentials by presenting quite an extreme version of Brexit. Some of the things that were being said were likely to have quite an impact outside the hall."
Senior EU figures were watching and concluded that the prime minister had outlined a series of undeliverable red lines.
The man who'd written the speech was May's powerful chief of staff Nick Timothy. A passionate leaver, he had also dreamed up "Brexit means Brexit" - a phrase that was much less empty than it seemed.
"I plead guilty to that phrase. It was one of the most irritating in British politics.
"Funnily enough it actually meant three different things. Firstly, that she understood that having been a remainer when the country voted to leave she would deliver on that mandate.
"It was [also] a warning to others - I think in particular in Parliament who were already showing signs of not really accepting the result - that Brexit must mean Brexit. Then at a third level that Brexit must meaningfully mean Brexit and couldn't be a kind of shadow membership."
Click here to watch Panorama: Britain's Brexit Crisis on BBC One, 18 July at 21:00
In the same speech, May announced that she would soon begin the formal process of leaving the EU by triggering Article 50. Hammond believes this was a mistake, given that there had been no real debate in the government, let alone the country, about what Brexit should mean.
"With the benefit of hindsight, I can now see that that was wrong," he says. "The real issue is debating with ourselves what kind of Brexit Britain wants.  And we should have done that before we triggered the process."
The chancellor says there was always going to be a tension between protecting the economy and "taking back control" of policies like immigration. It was a tension that was never fully resolved.
"... She hoped to improve her position and make it easier to deliver what people voted for in the referendum but actually the result made that job even more difficult."
Gavin Barwell lost his seat as a Conservative MP when Theresa May called a general election in June 2017. He was hired as her new chief of staff, replacing Nick Timothy - the man blamed by many for her decision to go to the polls. The election  left her with no majority in the House of Commons.
"Those first few weeks were a pretty traumatic experience," says Barwell. "That was apparent from the first day I walked into No 10."
The US President Lyndon B Johnson said: "The first rule of politics - you have to be able to count."
In other words, leaders need to be sure that they have more people backing their policies than opposing them.
The votes of Tory MPs alone would not now give May a majority. She turned to Northern Ireland's Democratic Unionist Party (DUP) for support. What she didn't do - until it was far too late - was to try to woo opposition MPs.  That was what Ted Heath had done before he took Britain into the Common Market in 1973.
Incidentally, it was not just May's closest advisers and cabinet ministers who helped convince her to call an election. Allies of Jean-Claude Juncker, a former prime minister himself, admit that while he would never have advised her to call an election, he did tell her that having her own mandate would help her.
Juncker warned that a tiny majority in a House of Commons that was less enthusiastic about Brexit than the British public would cause real problems when she eventually needed MPs to ratify a Brexit deal with the EU.
"...The UK chose itself the date for leaving in March 2019. This is why every time I just recall the clock is ticking. Be careful eh?"
 Again and again, Michel Barnier reminded British ministers that they would have just two years to reach agreement. It was clearly stated in Article 50 of the Lisbon Treaty that set the rules for how a country could leave the EU.  It allowed Brussels to use time against the UK.
 Senior figures in government have told me that the UK side misunderstood Barnier's real role. He was the public face of the negotiations and the politician who would keep the leaders of the EU's 27 countries on side.
Barnier's deputies did the real negotiating, alongside Martin Selmayr - the man whose nickname in Brussels is "the Monster" - who really decided what could and could not be agreed by the EU.
Selmayr explains the thinking behind the process for the Brexit negotiations, that would give the EU control not just of the timetable but also the agenda and the order [or sequencing] of the talks.
"Brexit will always be a sad event because it's a divorce. First of all you separate the assets… the rights and duties that are stemming from 40 years of a very long and intense and close relationship. Then you see if you remain friends afterwards or if you can remain close friends afterwards."
In 2017, Brexit Secretary David Davis promised a long hot summer when he would fight the idea that the UK would have to agree the Brexit bill it owed - which would run into tens of billions of pounds - before any talks could begin on a future trading relationship with the EU.
In the event the fight never occurred. He claims that he was overruled by May:
"She felt pressurised, unconfident, maybe even insecure after the general election outcome. She gave away the fact that we were going to meet everything they wanted - money and citizens' rights and so on - and get nothing back in return."
David Davis never persuaded the rest of the cabinet, let alone the prime minister herself, to make the threat summed up in another of her oft-repeated phrases - "no deal is better than a bad deal" - appear credible.
"The Treasury in particular would always argue you can't frighten the horses," he says. "Don't talk about it publicly, don't say what needs to be done, don't do the public preparation."
Davis complains that the chancellor was so nervous of spooking business that he stopped the Brexit department sending out letters to tens of thousands of small businesses telling them to prepare for a no-deal Brexit.
Hammond counters that he was trying to reassure business to stay in the country and to keep investing, so the last thing he wanted was anything that would have the appearance of no deal.
"There was a tension at the beginning. We didn't want to send business a message that we're going to crash out of the EU and see businesses perhaps relocating - taking jobs out of the United Kingdom."
The official projections were clear. A no-deal Brexit would lead to 10% tariffs on car exports, and 40% tariffs on the sale of lamb, says Hammond, as well as potential chaos at Dover with the French being able to "dial up and dial down" the queues at will to make a political point.
Hammond was not alone. One of the top officials handling Brexit told ministers that threatening no deal was like taking the pin out of a grenade and holding it next to your own head.
When I asked Michel Barnier if May or her ministers had ever made a no deal threat behind closed doors, he replied emphatically, "No", before adding, "I think that the UK side, which is well informed and competent and knows the way we work on the EU side, knew from the very beginning that we've never been impressed by such a threat. It's not useful to use it."
Selmayr agreed. "I don't think it's ever a reality for anybody who is in a responsible position. It has consequences. It ruins your relationship for the future and I don't think anybody responsible on the UK side or the EU side has an interest in that," he said.
In fact, when I asked Selmayr if he thought the UK was prepared for that eventuality, he said he was "very certain" it was not.
"We have seen what has been prepared on our side of the border for a hard Brexit," he said. "We don't see the same level of preparation on the other side of the border.
"... That would be in many ways a symbol of the past of tragedy, of emotion, of terrorism, of murder."
It was not just in Brussels that Brexit was seen as a threat.
In Dublin, Simon Coveney - who is now Ireland's Tanaiste, or deputy head of government - says he feared that there would be a return to a hard Irish border unless the issue was addressed right at the beginning of the negotiations.
Other senior figures in the Irish government have told the BBC that they were concerned that Ireland could be "dragged out" of the EU by its bigger, richer neighbour. That is why the backstop - the issue which came to dog Brexit - was born.
After Brexit, the border between Northern Ireland and the Irish Republic would be the only land border between the EU and the UK. If peace was to continue, everyone agreed that there should be no border controls. However, the EU's desire to protect its single market would mean there had to be checks on certain goods such as farm animals and chemicals that crossed the border.
The argument went that a post-Brexit Britain might do a trade deal with Donald Trump's US and could agree to allow the import of chlorine-washed chicken or hormone-treated meat. Without a border, those banned goods could move from north to south and into the EU, undercutting European food standards and representing cheap and unfair competition to their farmers.
Controls designed to enforce EU rules could become a target for paramilitaries and encourage smuggling which for years was key to the financing of terrorism.
If the UK followed EU rules and regulations, this wouldn't be a problem but Ireland and the EU demanded a guarantee - or a backstop - that whatever trade deal was eventually signed between the two sides there could never be a hard border.
Brexiteers saw this as a trap designed to keep the UK bound to EU rules and in a customs union. Talking to the BBC, the former Brexit Secretary Dominic Raab, sums up their fears:
"The idea that you could leave the EU, be successful and demonstrate that the EU perhaps wasn't all it was cut out to be was for them the thing that made [the EU]    the most nervous. And the obvious answer to that was to try and lock the United Kingdom in to as many EU rules as possible without any say over them and without any means to escape from that regime, and that's the conundrum of the backstop."
Raab's predecessor David Davis agrees with this position:
"They needed a lever which put us in the wrong and them in the right, I think that's the way they saw it. [With] the Irish border there's a strong political, moral, sentimental argument... based on fiction really, but nevertheless that's how it's used."
In other words the backstop was as much about trade as it was about peace. It was as much about French determination to protect the single market as it was about Irish worries about a new source of conflict. One of May's closest allies told us it was the "operationalisation by Brussels of a French idea dressed in a green jersey".
So why did the prime minister sign up to it? Because the clock was ticking and because she'd agreed to the EU's sequencing of the talks. No backstop meant no progress to talking about trade.
What's more, Theresa May was desperate to get agreement to the Treasury's top priority, which was the demand from big business for an extra two years to adapt to Brexit - the so-called transition period.
Davis blames No 10 for agreeing to the backstop. "They signed up to the backstop because they were desperate to make progress. They basically had a loss of nerve."
When we put to Martin Selmayr that the deal was "swallow what you don't much like on Ireland, and get more time", he replies: "Absolutely."
"Let's get the UK involved with France and Germany. Let's see how the dust settles and let's talk about whether we can come to a new deal for Europe."
Britain's de facto deputy prime minister David Lidington reveals to Panorama that he was made that startling offer by Martin Selmayr. It followed a summit of world leaders at which EU heads found themselves on the same side as Theresa May in a series of arguments with President Trump.
Selmayr explains why the offer was made:
"All the other European leaders were left behind when he [Trump] took the helicopter and they looked each other in the eyes and also at Theresa May and they thought, 'At least we all agree with each other, we are the last bastion of the rules-based international system.' I think that led to many thinking, 'Well, if she comes back tomorrow and has thought again, we wouldn't mind'."
Donald Tusk once joked in public about the idea that Brexit could be reversed saying, "Who knows? You may say I'm a dreamer, but I'm not the only one." However, this is the first time it has been confirmed that an approach and an offer was made by the European Commission to put Brexit on ice.
The offer was rejected and some in the EU came to the view it would be better if the UK left - and left quickly. However, the scale of opposition Theresa May faced in Parliament meant others continued to believe and hope that there would be another referendum and Brexit would not happen. This made them less likely to compromise.
"The two big parties have been trying to outmanoeuvre each other on Brexit, and for a long time Brexit has been used by the opposition party as a way of trying to trigger a general election. For me, as somebody who loves Britain, who's lived there, who's studied there, who has family there, I think it's a tragedy quite frankly, that in the face of this huge decision that the British people have made, that the political system has not been able to unite behind a middle-ground position and unite the country."
Simon Coveney is scathing about the failure of the British Parliament and political system to achieve consensus on Brexit. It's a stark contrast with the unity which has been on show in Dublin.
He blames the opposition Labour Party as well as the Tories. The government's Chief Whip, Julian Smith, says that he has lost a lot of sleep as a result of trying - and failing - to get a deal through the House of Commons.
"I think that there was definitely a shift from some Brexiteers who, if you'd asked them three years ago, would they be happy with the prime minister's deal, they'd have bitten your arm off. They then, during the course of the last year, became, I think, increasingly concerned about different elements of it, seeing some form of threat behind many aspects of it, and there was a kind of purification process - they sort of wanted everything on day one."
The Tories were hopelessly divided over what sort of Brexit deal to pursue. When May finally proposed her "Chequers plan" she did it without ensuring that she had the support of David Davis, her Brexit secretary .
Her allies believe that if Davis had been offered another job, he would have taken it rather than quitting the Cabinet altogether. They believe that Boris Johnson might then have stayed in the government.  As it was he became the figurehead for those wanting to "chuck Chequers" and, eventually, to chuck Theresa May as well.
The chief whip also blames the Speaker for blocking Brexit.  John Bercow ruled that the government could not bring back its withdrawal agreement to the Commons after it had been defeated twice. By this time, even hardliners like Boris Johnson and Jacob Rees-Mogg were prepared to vote with the government. No 10 insiders claim that they had the basis of an agreement which could have got DUP support as well but the vote was never held.
"Parliament is and has been deadlocked for one simple reason," says Julian Smith. "Large groups of MPs have been prepared to gamble that they could force the outcome they wanted - a harder Brexit or another referendum or a general election - rather than backing Theresa May's deal."
"If the only goal of the EU is this market obviously you could think that the German car industry could force the German government to comply with the demands coming out of London, but for Germany the EU is much, much more than a market. It's their destiny, it's not revisiting the horrors of history so even the car industry itself understands that this is fundamentally more important than selling cars to the United Kingdom."
EU leaders such as Frans Timmermans believe that British politicians do not understand the idealism and the history which underlies the European project. He says that "continental Europeans" do not see the EU in the same way as the United Kingdom - "as a market".
Brexiteers like Boris Johnson don't dispute the history but they do doubt that the leaders of any country would willingly harm their own economies. He has said in public that EU countries will want to sell us their cars or cheese or even Prosecco.
Did that claim infuriate Timmermans?
"Yes it did, also, perhaps I'm being a bit harsh but it's about time we became a bit harsh also because I'm not sure he [Johnson] was being genuine, I always have the impression he's playing games."
David Lidington - a lifelong pro-European - agrees that the EU has always seen itself as a political project but says it takes two to create a misunderstanding. He says that EU leaders have too often dismissed British demands as driven purely by short-term political pressures rather than principle:
"They thought Tories were simply pandering to UKIP or the DUP and never understood that Euroscepticism, a desire for sovereignty, support for the Union were real forces that any political leader and party would have to address."
Those misunderstandings have dogged the Brexit negotiations as both sides have miscalculated how the other side will react.
What has not been tested yet is whether the credible threat of no deal, a refusal to compromise on the Irish border and a willingness to withhold the £39bn divorce bill which Britain has agreed to pay will improve or destroy the chances of getting a deal.
We're about to find out.
Additional research and reporting by Britain's Brexit Crisis producer Max Stern

Donald Tusk does a good turn in press conferences, delighting headline writers by channelling song lyrics, making dramatic pauses. He, like his European Council colleagues, is a pro.
Even when he is saying something positive about the Brexit negotiations, he manages to convey his personal sadness about the fact the UK has decided to leave with a rather hang dog expression.
Today therefore, don't be surprised that the headlines out of his press conference to mark the publication of the EU's negotiating guidelines for our future trade relationship with them after Brexit are tough for the UK, his expressions hard reading for the government, and the guidelines themselves showing big gaps between the two sides as, to use his phrase today, we are "drifting apart".
The guidelines include, therefore, what the EU side would see as a reality check for the UK. In Brussels' view, there are, as one insider put it, "some vestiges of la la land" in the UK's position.
Today's paper demonstrates how sceptical the EU 27 is, for example, about the UK's hope to choose to stay in some European agencies.
Again, Mr Tusk has said that the UK's overall hope to pick and choose bits of the European apparatus is a non-starter. But before the next formal round of negotiations have begun it would be a genuine shock if he were to say anything else.
On the UK side, the EU has what one insider suggested were "significant' cojones", to suggest for example that the EU retains fishing rights in UK waters. And while not exactly jumping for joy, nor is the government in meltdown over the EU's opening gambit.
The details of the guidelines are here, complete with Donald Tusk's warnings.
But is this a giant two fingers to Theresa May's entire approach that really changes things for the negotiations? Have they today completely torn up the Mansion House speech?
There are significant differences of course, and I'm not suggesting for one second that the way forward is clear. But no one in government will be hugely surprised by the publication today, nor do they believe that it is time to run up the white flag.
In fact, the two sides notionally agree that they are both looking for an ambitious trade deal. Having repeatedly ruled out staying in the Single Market or the Customs Union, that is what the prime minister says she wants. And the EU has said it is willing to talk on the basis of there being no tariffs or quotas either.
Back in the depths of the referendum campaign, that would have seemed like quite a prize. And crucially, the draft guidelines hold out a small promise of room for manoeuvre, saying "if the UK positions were to evolve, the EU would be prepared to reconsider its offer".
In the coming months that may prove the most important paragraph of all. If the UK is willing to compromise, well the EU might have a rethink too.
The document may well be a reminder that it's the UK that will have to do most of the budging, but the draft guidelines do suggestion there is at least a conversation to be had.

A petition on Parliament's website calling for Brexit to be cancelled has now passed more than 5.7m signatures.
The petition to revoke the Article 50 withdrawal process has gained more than one million signatures since Saturday's march calling for a new EU referendum.
Theresa May has stressed that the UK had already decided to leave the EU in the biggest ever democratic exercise.
But European Council chief Donald Tusk has said revoking Brexit was an option if MPs again rejected the PM's deal.
The UK has to decide its next move by 12 April after the EU agreed a plan to delay Brexit beyond 29 March.
The prime minister hopes to bring the agreement she has negotiated with the EU back to the Commons for the third time but MPs want other options to be considered as well - and on Monday backed a series of votes to find out the kind of Brexit deal they would support.
In December, the European Court of Justice ruled that the UK can unilaterally revoke Article 50 of the Treaty of the European Union, the clause which allows a country to leave the bloc.
This means the UK can decide to stay in the EU without the consent of the 27 other member states.
Lib Dem MP Layla Moran has said the petition could "give oxygen" to the campaign for another Brexit referendum, a so-called People's Vote.
However, speaking on Thursday night after the petition reached the two-million mark, Mrs May said the public had already had their say on EU membership.
"They voted in 2016, they voted to leave. I think the time is now to deliver for the British people, the time is now to make the decision," she said.
People signing petitions on the Parliament website are asked to tick a box saying they are a British citizen or UK resident and to confirm their name, email address and postcode to sign.
The petition was started in February and quickly passed the 100,000-signature threshold needed for it to be debated in Parliament. It began to attract thousands of more signatures last week and at one stage caused the petition website to crash.
It reached four million signatures on Saturday, as hundreds of thousands of people marched in central London, making it the most popular to have been submitted to the parliament website.
A petition for a second EU referendum in June 2016 attracted more than four million signatures and was debated in the Commons - but thousands of signatures were removed after it was discovered to have been hijacked by automated bots.
In January, MPs debated whether the UK should leave the EU without a deal, after a petition calling for that got 137,731 signatures.

The UK will be unable to buy privileged access to the single market after it leaves the EU, says one of the top UK officials to have worked in Brussels.
Jonathan Faull, who retired last week, said that access to the single market "is not something that's on sale".
He also warned the UK should not assume it can  broker a deal with Angela Merkel if she wins re-election as German chancellor.
Theresa May plans to trigger the Brexit negotiations by the end of March.
But Mr Faull said that Britain has one important card to play in the EU negotiations - co-operation on European defence.
The warnings by Mr Faull, who served in the European Commission for 38 years, come as the government scrambles to assemble its Brexit negotiating team in the wake of the resignation of the UK's EU ambassador, Sir Ivan Rogers.
He is to be replaced by Sir Tim Barrow, a former UK ambassador to Moscow.
In his interview with BBC Newsnight, Mr Faull cast doubt about an idea, which is being promoted by senior Whitehall officials, that the UK could pay for privileged access to the EU's single market.
This would be designed to circumvent the rules of the single market whose members, including Norway which is outside the EU, have to accept the free movement of people and the jurisdiction of the European Court of Justice.
David Davis, the Brexit secretary, confirmed last month that the government was considering the idea.
Mr Faull said: "Can you buy access to the single market? It's not something that's on sale in that way. I find that rather extraordinary."
The former European Commission official pointed out that Norway is bound by two core rules of the EU - accepting the free movement of people and abiding by the European Court of Justice.
Theresa May has indicated that she would like to have some access to the single market. But the prime minister is to confirm in a speech later this month that the UK will have two fundamental red lines in its Brexit negotiations - control of its borders and freedom from the ECJ.
Mr Faull suggested that if the UK cannot accept the fundamental rules of the single market it would be regarded as a foreign country: "I don't think it is a question of buying your way somehow into the single market."
"You're a member of the single market as a member of the EU or the EEA. Or you're a foreign country outside it, and you conclude agreements with the EU - if you want to and it wants to - regarding the way in which your goods, services, capital and people move around.
"Or you don't and you have one or two international rules which apply and that's it, that's a choice to be made by both sides."
Newsnight was speaking to Mr Faull as part of a profile of Michel Barnier, the former French foreign minister who is the EU's chief Brexit negotiator.
Downing Street expects Barnier to adopt a hardline stance once the Brexit negotiations are formally under way when Theresa May triggers Article 50 of the Lisbon Treaty.
But in private, ministers believe that Angela Merkel will take a more benign approach if she wins re-election as German chancellor later this year.
Mr Faull warns that Theresa May's government could be in danger of repeating the mistake of David Cameron who believed that Mrs Merkel would come to his rescue. Mr Faull was the senior European Commission official involved in the Cameron negotiations.
"I think it would be a mistake to see the EU institutions as somehow wholly different from the 27 countries. These are all actors that will be working together on this," he said.
"I think one should look perhaps at the experience of the negotiations which took place before the referendum. where perhaps some similar thoughts were expressed and turned out not to be fully realised."
Mr Faull's remarks were endorsed by Lord Patten of Barnes. The former European commissioner told Newsnight: "There's an awful lot in the British press about what we'll get from them, what we'll negotiate from them. And I think it overlooks the fact - and I'm not making a 'why we should remain' point - the fact is they'll decide."
"They'll decide and we must hope that we can get as decent a deal as possible. But it's ultimately going to be decided in Paris and Berlin and some of the other member states."
But Mr Faull said that Mr Barnier will be well disposed to the UK in one key area - co-operation on defence led by France and the UK, Europe's two largest defence powers.
He said: "Michel Barnier has done a lot of work in recent years on defence and strategy issues and he believes the UK is absolutely crucial to the defence and security of Europe, the continent."
"And Franco-British cooperation in defence and security matters is extremely important and he will want - and I think all Europeans will want - a way to be found for that to continue."
"But that's more complicated if you're outside the EU, because part of the mechanisms used for this purpose are today EU mechanisms - so all of that will have to be looked into."
Nicholas Watt is political editor for BBC Newsnight

Airbus has warned it could leave the UK if it exits the European Union single market and customs union without a transition deal.
The European planemaker said the warning was not part of "project fear", but was a "dawning reality".
Airbus employs 14,000 people at 25 sites in the UK - around half in Wales.
The UK government said it was confident of getting a good deal for all industries, but the Welsh government said it was "extremely worrying".
In its Brexit "risk assessment" published on Thursday, Airbus said if the UK left the EU next year without a deal - meaning it left both the single market and customs union immediately and without any agreed transition - it would "lead to severe disruption and interruption of UK production".
"This scenario would force Airbus to reconsider its investments in the UK, and its long-term footprint in the country," it added.
The company, which makes wings for the A320, A330/A340, A350 and A380 passenger planes in the UK, also said the current planned transition period, due to end in December 2020, was too short for it to make changes to its supply chain.
As a result, it would "refrain from extending" its UK supplier base. It said it currently had more than 4,000 suppliers in the UK.
The customs union brings together the EU's 28 members in a duty-free area, in which they pay the same rate of duty on non-EU goods
Prime Minister Theresa May has ruled out staying in the customs union. The UK is due to leave the EU on 29 March 2019.
The UK government is considering two other options: a customs partnership that would remove the need for new customs checks at the border; and a "highly streamlined" customs arrangement that would minimise customs checks rather than getting rid of them altogether.
Michel Barnier, the EU's Brexit negotiator, has said that both options are unrealistic.
A spokesperson for Prime Minister Theresa May said: "We are confident that we are going to get a good deal, one that ensures that trade is as free and frictionless as possible, including for the aerospace sector,"
A Welsh government spokesperson said: "We have repeatedly warned that the UK cannot take the huge economic risk of cutting ourselves adrift from the single market and customs union. Particularly in the case of manufacturing sectors, which in Wales are so important in providing high-paid, high-skilled jobs."
Simon Jack, business editor
It has been a source of exasperation for some cabinet members that although many companies have privately expressed concern - even alarm - at the progress of the Brexit negotiations, they have been reluctant to make their fears public, and have even dialled down the shrillness of their warnings when meeting the prime minister in person.
Airbus' decision to warn that future investment in their operations in the UK are under review, while not exactly welcome, is therefore considered by some in government as an honest and helpful declaration of what's at stake for UK workers and the wider economy.
Prominent Brexit supporter Sir Bernard Jenkin described Airbus' comments as the kind of "speculation" seen before, during and after the referendum from large companies. But Airbus' UK boss, Katherine Bennett, told the BBC, "this is not project fear, this is dawning reality".
Tom Williams, chief operating officer of Airbus Commercial Aircraft, said in "any scenario", Brexit had "severe negative consequences" for the UK aerospace industry and Airbus in particular.
Without a deal, he said Airbus believed the impact on its UK operations could be "significant".
"Put simply, a no-deal scenario directly threatens Airbus' future in the UK."
Airbus's main civil aircraft business is based in a suburb of the French city of Toulouse. Apart from France and the UK, it has production and manufacturing facilities in Germany, Spain, China and the US.
Mr Williams told the BBC's Today programme that Airbus was currently working on developing the "next generation" of aircraft wings in the UK.
"We are seriously considering whether we should continue that development or whether we should find alternative solutions," he added.
Conservative MP Stephen Crabb said the warning from Airbus should be a "wake-up call".
Mr Crabb tweeted: "The enormous Airbus factory in North Wales is one of the jewels in the crown of UK manufacturing. This is a wake-up call. A pragmatic, sensible Brexit that protects trade & jobs is vital."
And shadow Brexit secretary Sir Keir Starmer tweeted: "If proof was needed that the PM's Brexit red lines need to be abandoned (and fast), this is it."
Liberal Democrat leader Sir Vince Cable described the Airbus warning as "the 'Oh my God' moment where something real is happening".
He added: "Airbus are making absolutely clear that if there is a risk of a hard Brexit, they will have to stockpile parts. They can't take the risk.
"A hundred and ten thousand jobs depend on this company.  About one-and-a-half billion in tax revenue that will not go into the NHS.
"We're now beginning to get serious about what Brexit means."

"The last call"... "we cannot wait any more"... "huge and serious" gaps.
European leaders can repeat the same message, louder and louder.
But this EU summit's instructions to Theresa May may as well have been shouted into an empty cupboard.
Because they know what she knows - that the past 24 hours of Brexit conversations are not nearly as important as the next seven days of discussions at home between Number 10 and the rest of the government.
And after more than two years, this time next week ministers should be nearing the conclusion of their country retreat at Chequers.
It's there that the prime minister hopes to find resolution in her team on a more detailed offer to the rest of the EU - easing, if not removing, all the contradictions in the Tories' positions.
Any pretence that the cabinet agrees is long gone.
The government's promised publication of their choices within days, which if comprehensive and detailed as promised, will mark a big step forward, and in theory allow progress towards a final deal.
But if the eventual Brexit white paper is flimsy - still a list of tentative options - patience in Brussels may finally run out.
Sources suggest that if there is no clarity from the UK next week, all that will be available to Britain is a simple free trade deal.
For many months, Theresa May has held the ring while inside her party brawls over Brexit have raged.
If she can't end the fight, by picking a winning side or forcing a persuasive compromise, the EU may call time.
In the next seven days the prime minister has hurdles she must clear to secure her future.

The prospect of Brexit happening without any deal being reached between the UK and the EU is "unthinkable", Home Secretary Amber Rudd has said.
Ms Rudd was responding to a question about the impact on security of nothing being agreed before the UK leaves.
"We will make sure there is something between them and us to maintain our security," she assured MPs.
Earlier Brexit Secretary David Davis defended keeping the "no deal" option open in the on-going negotiations.
After five rounds of Brexit negotiations, the EU has described the talks as in "deadlock" and there has been an increased debate about the possibility of the UK leaving without a deal in place.
One of the UK's aims is for a new security treaty with the EU, and Ms Rudd told the Commons Home Affairs Committee contingency plans were being made in case this was not in place by the UK's departure in March 2019.
Asked whether, if there was "no deal of any form", Britain would be as safe and secure as it currently is, she replied: "I think it is unthinkable there would be no deal.
"It is so much in their interests as well as ours - in their communities', families', tourists' interests to have something in place."
Ms Rudd also said it was "unthinkable" EU citizens would be asked to leave the UK after Brexit, but was unable to offer guarantees while negotiations continue.
Mr Davis was asked about a "no deal" scenario as he updated MPs on Monday's dinner between Theresa May and EU officials.
Reaching agreement with the EU is "by far and away the best option" he said, adding: "The maintenance of the option of no deal is for both negotiating reasons and sensible security - any government doing its job properly will do that."
International Trade Secretary Liam Fox said there was no reason to fear the impact on the economy of no deal being agreed, saying it "would not be the Armageddon that people project".
He told the BBC: "I think that we need to concentrate on the realities, get rid of the hyperbole around the debate and focus on the fact that if we can get a good agreement with the EU, both Britain and the EU would be better off for it."
A UK-EU free trade deal cannot be discussed until the EU deems sufficient progress has been made on other matters and gives the green light.
In his statement to MPs, Mr Davis said the UK was "reaching the limits of what we can achieve" in Brexit talks without moving on to talk about trade.
He urged EU leaders to give counterpart Michel Barnier the green light at this week's EU summit to begin trade talks.
Mr Barnier said he wanted to speed up talks but "it takes two to accelerate".
This was a reference to comments made by Mrs May after her dinner with the EU's chief negotiator, in which she said the two sides had agreed on the need to "accelerate" the process.
Speaking on Tuesday, Mr Barnier said a "constructive dynamic" was needed over the next two months but "there was a lot of work to do" and issues must be tackled in the "right order".
"At the moment we are still not yet at the first step which is securing citizen rights, guaranteeing the long term success of the good Friday agreement and finalising the accounts," he said.
The talks - which were held as EU member states prepare to assess progress so far on Thursday - were said to be "constructive and friendly" but the UK's financial settlement with the EU continues to be a sticking point and the EU will not discuss trade until this has been settled.
Along with the UK's "divorce bill", the EU is insisting agreement be reached on citizens' rights and what happens on the Northern Ireland border before agreeing to open talks on the free trade deal Mrs May's government wants to strike.
In his Commons statement, Mr Davis urged the EU to give Mr Barnier a mandate to start discussing its future relations with the UK, including trade and defence, telling MPs he was "ready to move the negotiations on".
He suggested the UK was "reaching the limits of what we can achieve without consideration of the future relationship".
"Our aim remains to provide as much certainty to business and citizens on both sides. To fully provide that certainty, we must be able to talk about the future."
On citizens' rights, he said key issues such as the rules on family reunion, the right to return, the onward movement of British expats in Europe and the right of EU residents to export benefits had still to be settled.
Announcing that EU citizens who currently have permanent residence in the UK would not have to go through the full process of re-applying before Brexit, he said the UK had consistently "gone further and provided more certainty" on their status than the EU had done.
While the UK had "some way to secure the new partnership with the EU", he was "confident we are on the right path".
Speaking in the Commons earlier on Tuesday, Foreign Secretary Boris Johnson said he thought a reported bill of £100bn was too high and urged the EU to "get serious" and agree to settle the citizens' rights question.
For Labour, shadow Brexit secretary Sir Keir Starmer said EU and UK citizens were still no wiser over their future while it "appeared the deadlock over the financial settlement is such that the two sides are barely talking".
"Nobody should underestimate the seriousness of the situation we find ourselves in. At the first hurdle, the government has failed to hit a very important target."
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Home Secretary Amber Rudd has hit back at Tory Brexiteers over attacks on the civil service and claims of disunity.
Ms Rudd said backbencher Jacob Rees-Mogg was "wrong" to accuse the Treasury of "fiddling the figures" with forecasts showing the UK would be worse off outside the EU.
The leaked forecast that sparked the row was a cross-departmental "tool" to "help inform the debate", she said.
And she said ministers were more united over Brexit than critics claim.
Speaking on the BBC's Andrew Marr show, she said she was "not intimidated" by Brexiteers' warnings over the customs union and that the UK government would not "surrender too quickly" in its battle for a "bespoke" trade deal with the EU.
Negotiations are taking place between the UK and the EU ahead of the UK's scheduled exit in March 2019.
Ahead of a week of key meetings, Theresa May is facing growing calls to set out in detail what she wants to secure - in particular how closely-bound the UK will be to the EU after it leaves.
Writing in the Sunday Telegraph,  Bernard Jenkin, a Conservative MP who was a key Leave campaigner, accused the government of being "vague" and "divided" on the issue.
But Ms Rudd told Andrew Marr she had "a surprise for the Brexiteers", that the key Brexit committee of ministers was "more united than they think".
The cabinet agrees on the need for "frictionless trade", the ability to strike international trade deals and avoid a hard border in Ireland, she said.
And on the key point of the customs union - which currently prevents the UK from striking international trade deals - she suggested "a form of customs agreement" would be needed.
Last week International Trade Secretary Liam Fox said it was "very difficult" to see how staying in a customs union would allow the UK to have an "independent trade policy" after Brexit.
BBC political correspondent Susana Mendonca
The accusations of cabinet divisions and disunity have kept coming from Brexit-supporting MPs over the past week. Now the home secretary has pushed back, saying the cabinet is "more united than they think".
If that is the case, the cabinet will be expected to demonstrate some of that unity this week when discussions between Theresa May, David Davis and EU negotiator Michel Barnier are bound to throw up some bones of contention - the transition deal being the main one. Will the cabinet be singing from the same hymn sheet on that? And what about the customs union, another thorny issue that key ministers have very different views on?
To silence its detractors, the cabinet will have to demonstrate this week it is neither "vague" nor "divided" - but whatever approach it comes up with is likely to lead to divisions with those who think they are going too far or not far enough.
The role of the civil service has been thrust into the limelight in recent days by a leaked analysis predicting an economic hit to the UK after Brexit.
Ms Rudd said the report did not "model everything" and predicted the UK economy would "absolutely grow" after Brexit, but said putting up trade barriers would have "consequences".
Describing the civil service as the envy of the world, she added: "We have to have these forecasts before making decisions."
She said she had been "surprised" at Mr Rees-Mogg's remarks and added that ministerial Brexit colleague Steve Baker - who has clashed with Whitehall unions and apologised to Parliament - had had an "interesting week".
Mr Baker's apology followed a Commons exchange after which he was accused of not challenging Mr Rees-Mogg's suggestion of Treasury bias against Brexit.
On the BBC's Sunday Politics, Conservative Party Chairman Brandon Lewis echoed Ms Rudd in saying Mr Rees-Mogg was wrong and defending Whitehall.
Former top civil servants have also hit back at critics.
Speaking on ITV's Peston on Sunday, ex-cabinet secretary Lord O'Donnell said claims officials were distorting figures were "crazy".
People who do not like their analysis tend to shoot the "messenger", he said.
"We look at the evidence and we go where it is.
"Of course if you are selling snake oil, you don't like the idea of experts testing your products."
His predecessor Andrew Turnbull, who was cabinet secretary under Tony Blair, told the Observer that attacks on the civil service were similar to tactics used by German nationalists between the two world wars.
BBC business reporter Rob Young
Customs union members each apply the same tariff to goods bought from outside the EU. Goods from inside the EU are not subject to tariffs.
Theresa May says Britain is leaving the customs union - so what will replace it?
For a lot of firms, customs rules are just as important as a trade deal. Brexit could disrupt many supply chains, if businesses buy parts from Germany or Italy, for example. Many exporters want a new customs deal with the EU to reduce the need for border checks - limiting queues and paperwork. But this could restrict Britain's ability to strike international trade deals outside the EU.
Some worry this undermines one of the key potential benefits of Brexit.
Customs are also key to the future border with Ireland. No wonder this is one of the thorniest issues arising from Brexit.
The UK and the EU do not currently agree on whether EU citizens moving to the UK during the planned two-year transition period after Brexit should get the same long-term rights as those who arrive before the UK leaves.
Defending the UK's position, Ms Rudd said it was "right to have a distinction between before March 2019 and afterwards".
Chancellor Philip Hammond has been the focus of much of the criticism from Brexiteers in the Conservative Party, and in his Telegraph article Mr Jenkin suggested Mr Hammond was not toeing the party line.
"If ministers are vague or divided, life for officials becomes impossible, as we can see now. Ministerial collective responsibility really matters," he said.
He added: "If the prime minister sticks to one policy and the chancellor keeps advocating another, what are officials meant to do?"
Earlier this month, Mr Hammond suggested the UK's relationship with the EU would change only "very modestly" after Brexit.
But Mr Jenkin urged the prime minister to stick to her position and ensure, among other things, Britain leaves the single market and customs union.
He wrote: "She can only command a majority in Parliament on her present policy.
"Her MPs will back her, because we are overwhelmingly at one with the majority of the British people who now want a clean Brexit and an end to the present uncertainty."

Amber Rudd has quit Boris Johnson's cabinet, with an outspoken attack on the government's approach to Brexit.
The ex-work and pensions secretary said the government was having no "formal negotiations" with the EU about a new deal, only "conversations".
Instead, 80-90% of Brexit work was spent preparing for an "inferior" no-deal option, she said.
But Chancellor Sajid Javid said ministers were "straining every sinew" to get a deal with the EU.
He told the BBC's Andrew Marr Show a "tremendous amount of effort" had gone into securing a revised deal.
Mr Javid added that preparations for a no-deal scenario would "concentrate minds" in Europe regarding working towards a new agreement.
Downing Street says environment minister Therese Coffey will replace Ms Rudd as work and pensions secretary.
BBC political correspondent Jonathan Blake said the prime minister spent Sunday meeting his closest advisers at the government's countryside residence Chevening House, in Kent, "perhaps planning the next move".
Ms Rudd told the Sunday Times she would be considering whether to stand as an independent Conservative should there be an general election.
In her resignation letter to the prime minister, Ms Rudd said: "I joined your cabinet in good faith: accepting that no-deal had to be on the table, because it was the means by which we would have the best chance of achieving a new deal to leave on 31 October.
"However, I no longer believe leaving with a deal is the government's main objective."
She called the PM's decision to expel 21 MPs from the parliamentary Conservative party an "act of political vandalism", after her former colleagues rebelled last week over a bill designed to avoid a no-deal Brexit.
"If we become a party which has no place for the type of moderates that I am, the centre-right Conservatives, then we will not win [a general election]," she said.
by John Pienaar, BBC deputy political editor
Amber Rudd's resignation was symptomatic of a deeper struggle going on inside the government and inside the Conservative Party.
Whatever anyone says, a number of ministers are considered to be privately unhappy with the government's strategy and contemplating the possibility of resigning in the wake of Amber Rudd's resignation.
The former chancellor, Philip Hammond, was saying this weekend that usurpers were turning the Tory party into an extreme right-wing sect.
He was clearly referring to people like the prime minister's famously abrasive, divisive adviser, Dominic Cummings.
But there's no sign of the inner circle in No 10 relenting or repenting - just the opposite.
One minister said to me today: "Look at the opinion polls. Tories well ahead - it's working." Losing colleagues, to him, was collateral damage.
Ms Rudd, the MP for Hastings and Rye, who supported Remain in the 2016 referendum, has resigned the Tory whip - meaning she will remain an MP but no longer sit as part of the Conservative party in Parliament.
She told the BBC there was "very little evidence" the government would get a new Brexit deal, and she had only received a "one-page summary" of efforts to get an agreement when she asked for details earlier this week.
She said "proper discussions about policy" had not been taking place, suggesting senior ministers had limited involvement in the PM's decisions.
Cabinet ministers had also not been shown legal advice to the prime minister about his decision to prorogue - or suspend - Parliament from next week until 14 October, Ms Rudd said.
Asked who was running the country, if not the cabinet, she replied: "If I knew that, I would perhaps have had further conversations with the prime minister, or them."
However, Mr Javid said there had been "progress" in talks with the EU about making changes to former PM Theresa May's Brexit deal, which was rejected three times by the House of Commons.
He said the government has "many new ideas" for proposals to break the deadlock over the contentious backstop plan in the deal aiming to preserve seamless border on the island of Ireland.
However he said it would be "madness" to talk through the details of the government's proposals openly.
"Anyone who understands how negotiation works, you would not discuss those in public," he added.
Former Foreign Secretary Jeremy Hunt said Ms Rudd's departure was "desperately sad news", describing her as "one of the most principled and capable ministers I've worked with".
Former Chancellor Philip Hammond tweeted that the Conservative Party had been "taken over by unelected advisors, entryists and usurpers".
Shadow Brexit secretary Sir Keir Starmer tweeted that her departure showed Mr Johnson's government was "falling apart".
Labour Party chair Ian Lavery said the resignation was a sign that "no one trusts" Mr Johnson. "The prime minister has run out of authority in record time and his Brexit plan has been exposed as a sham," he said.
SNP Westminster leader Ian Blackford called on the prime minister to resign, arguing he had "no support or credibility left".
But Foreign Secretary Dominic Raab said Mr Johnson had made clear to all his cabinet ministers they needed to support his policy of leaving the EU by 31 October, in all circumstances.
"We all accepted that, and I think the prime minister was right to restore some discipline - and I think he's right to expect it from his top team," he told Sky News.
In other developments:
Monday
Wednesday:
Thursday:

It's not a snub.
Or a rule-breaker.
Or a witches' cauldron around which anti-UK tactics will be plotted.
Theresa May doesn't invite the European Union to her Brexit strategy discussions - as you might expect - and the EU doesn't invite her to theirs, for the very same reasons.
As a full member (still) of the EU, the UK prime minister is included - as she must be - in today's formal summit of all 28 EU leaders.
Mrs May will be present for discussions on migration, Aleppo, Ukraine trade and Russia sanctions.
But once that is over and summit press conferences have been held, EU leaders will meet without the UK for an "informal dinner" where the menu reads: Brexit from hors d'oeuvres to dessert.
The timing of this dinner is a diary convenience.
Getting 27 world leaders round one table isn't easy, especially when a number of them are fighting for political survival at home.
So, while together in Brussels anyway for the summit, Chancellor Angela Merkel, President Francois Hollande et al agreed to stay a bit longer to talk Article 50, the by-now long-awaited triggering by the UK of formal Brexit talks, that Mrs May promises early next year.
Dinner tonight, my sources tell me, will be all about procedure.
The EU27 (as the leaders minus the UK now call themselves) will formally re-confirm the European Commission as the lead Brexit negotiator for the whole European Union.
Make no mistake, in such a complex and politically important process, Germany, France and other EU countries will keep a very close eye on the Commission but they know it is the only EU institution with the manpower, the expertise (it leads all EU trade negotiations) and a legal mandate (as so-called guardian of EU Treaties) for detailed negotiations.
So much for Brexit procedure; as for content over tonight's nibbles, my sources insist there's little to discuss until the UK government makes a firm commitment to the kind of Brexit it wants.
UK Brexit Secretary, David Davis, for example, just came up with four possible scenarios as regards the European Customs Union.
But EU leaders are clearly nervous.
Brexit has become a political football as populist movements gather strength across Europe.
Many leaders are also irritated with the perceived arrogance of the UK government - whether it's the foreign secretary insisting that EU Single Market rules will be bent for the UK or the Brexit Secretary suggesting an interim trade deal might be accepted out of kindness to the EU, rather than the other way round, which is the perspective of Brussels.
Over and again I'm told: we never wanted the UK to leave. It chose to go. We now need this over and done with so Brexit no longer hangs over all EU affairs.
EU governments insist they want an end deal that's good for everyone. They're keen to keep Britain close. But they do expect the UK to respect EU law. That means, as we've heard: no access to the Single Market if the UK won't accept the right of EU citizens to apply live and work in the UK.
On this point, EU countries and the Commission sing from the same hymn sheet.
They all benefit from the Single Market and they worry about weakening it.
But, desperate as they are to insist that theirs is a fully united front, there will undoubtedly be Brexit bickering amongst tonight's dinner guests.
One high-level source described Article 50 to me as "the mother of all complexities".
Some European Prime Ministers (particularly from the Baltic States and central Europe) worry the Commission will be too hard line. They want open talk of a transition deal and believe Article 50 proceedings should be about the future EU-UK relationship, not just the divorce.
Many EU leaders chatting about Brexit tonight know they're unlikely to see the process through.
Elections are fast-approaching in France, the Netherlands and Germany. Possibly in Italy too.
Today the BBC revealed a memo to the government by a high level British civil servant warning Brexit could take years and even then be voted down by an EU country or institution.
Something the EU warned about from the start.
Still, a Brussels source said to me it'll be far speedier if hard-line Brexiteers win the day and the UK reverts to WTO trade rules.
No transition deal needed then, he said.
Another Brussels voice believed Russia sanctions discussions at today's EU summit would show Theresa May that she has more in common with the EU than she realises.
The year 2017 is going to be a lot about Russia, my contact insisted.
"Prime Minister May will find us a lot more Russia-reliable than the soon-to-be US president, Donald Trump."
"Though the UK never appreciated its EU relationship as 'special'," he noted (not without a note of bitterness).

This didn't seem a comfortable moment for Dominic Raab.
The Brexit secretary campaigned for Leave, and is a true believer in the cause. Yet here he was, setting out plans to cope with a British failure to reach the kind of deal Brexiteers once claimed would be easy to accomplish.
Again and again, the Brexit department's guidance refers to the "unlikely event" of Brexit without an EU deal - but Dominic Raab conceded it could happen.
The risk was real. The International Trade Secretary, Liam Fox, has suggested that outcome is more likely than not. The Brexit secretary may disagree on the level of risk, but could not deny that it would lead to higher costs and a fresh burden of red tape on businesses, scientific and medical research and individuals.
In today's first tranche of advisory papers on how to handle a no-deal Brexit, we learned card payments in Europe could cost more, as the EU cap on charges disappeared. That would add to the holiday and travel expenses of millions of Brits.
There was no guarantee yet of Brits and other UK dwellers on the continent having the same access to bank accounts and pension payments. Again Mr Raab was looking on the bright side. Why would the EU refuse to co-operate and risk piling identical burdens on Europeans in Britain.
The list went on. And on. Medicines were being stockpiled - though that didn't rule out the possibility of shortages.
And on the potential effect on UK firms involved in trade with the EU, the message was no less striking for being an inevitable consequence of quitting the EU single market and operating under the rule of the World Trade Organisation in the absence of a free trade agreement. Exporters would face an entirely new system of customs duties and safety declarations at a stroke. Consultants would need to be consulted. Software bought. Contracts rewritten.
Yes, farmers who receive EU subsidies could count on those payments being continued by a newly liberated Department for the Environment, Food and Rural Affairs. Whether the same farmers would be entirely happy with the new schedule of tariffs on agricultural imports and exports is another matter, and not discussed today.
The list of new home-grown rules and regulatory agencies was huge. Mr Raab's hope was that the EU would co-operate with and recognise this new sprawling network of agencies and authorities, not for Britain's sake, but in its own interests. Maybe. But who knows?
The minister hoped and believed an agreement was still the most likely outcome. The two sides, he said, were "within sight" of a deal. Some close to the process might consider that an optimistic assessment. Theresa May's Chequers plan - a single market for goods but not services among other things - seems to have fallen rather flat in Brussels.
Dover is, after all, "within sight" of Calais. The political distance may turn out to be unbridgeable. So far, there's no sign of Brussels weakening on its negotiating "red lines". Today's "no-deal" plans may seem extensive, and there is much more to come.
To Dominic Raab the idea that everything will work out in the end seems plain common sense. The potential disruption and costs former Remainers and Brexit sceptics see as national self-harm, Brexiteers see as a few bumps in the road en route to a brighter future.
Dominic Raab may be a more comfortable colleague for the prime minister to deal with than his predecessor, David Davis, but he is a true believer nonetheless. You could call his conviction a product of faith. Or, if you prefer, call it wishful thinking.

EU leaders who gathered in Brussels put on a united front to back Theresa May's argument that the withdrawal agreement they endorsed was the "best and only" Brexit deal available.
But there was no sense of celebration, and there were plenty of signs of how tough negotiations on the future EU-UK relationship are likely to be.
Alongside the withdrawal agreement, and the political declaration on future ties, the remaining 27 EU leaders published a separate statement (without the UK) that vowed to protect their own interests, on a range of issues from fishing to fair competition to the rights of citizens.
"The European Council," it said, "will demonstrate particular vigilance as regards safeguarding the rights and interests of citizens, the necessity to maintain ambitious level playing field conditions, and to protect fishing enterprises and coastal communities."
It emphasised in particular that a fisheries agreement that builds on "existing reciprocal access and quota shares" is a matter of priority.
The statement was a clear sign that the UK will not have things all its own way, when it comes to balancing the competing demands of access to EU markets for UK fish produce, and access to UK fishing waters for EU boats.
Several EU leaders highlighted fishing as a particularly sensitive issue. German Chancellor Angela Merkel said talks on fisheries were "undoubtedly going to be an area where negotiations are going to be tough".
But the bluntest warning came from the French President Emmanuel Macron, who suggested that if the UK was unwilling to compromise in negotiations on fishing, which would need to make rapid progress, then talks on a wider trade deal would be slow.
"We as 27 have a clear position on fair competition, on fish, and on the subject of the EU's regulatory autonomy, and that forms part of our position for the future relationship talks," he said.
The president implied that without sufficient progress on trade, the backstop plan to avoid a hard border in Ireland would have to be implemented, including a temporary customs union for the whole of the UK.
"It is a lever because it is in our mutual interest to have this future relationship," Mr Macron said.
"I can't imagine that the desire of Theresa May or her supporters is to remain for the long term in a customs union, but (instead) to define a proper future relationship that resolves this problem."
It is a warning that the prime minister could have done without, as she seeks to appeal to the British public for support for her deal in advance of a vote in Parliament next month.
But it is also a reminder - if any were needed - that other countries have domestic political concerns that will have to be taken into account.
If anything, the negotiations on the future relationship - which can only begin formally after the UK has left the EU - will be even harder than the 18 months of negotiations that produced the withdrawal agreement which has just been endorsed.

Andrea Leadsom has said that the EU may be prepared to grant the UK a "couple of extra weeks" beyond the 29 March deadline to finalise preparations for Brexit.
The Commons leader said that in light of the UK's strong relationship with its "EU friends", the UK could be allowed more time for an approved deal to pass all its parliamentary stages.
But Ms Leadsom accused the EU of being in denial about the unease in the UK over the Northern Ireland backstop.
In a rebuke of Amber Rudd and Philip Hammond, the Commons leader called on the cabinet to rally behind Theresa May and accept that the UK will leave the EU without a deal if MPs reject her deal.
In an interview with BBC Newsnight, Ms Leadsom said she had "grave concerns" about a bill, proposed by Labour MP Yvette Cooper, which could extend Article 50 by nine months.
But she said that the EU could agree to allow the UK to remain in the EU for a few weeks longer than the March deadline. This could happen if a deal has been reached, but more time is needed for parliament to approve its Brexit legislation.
A Downing Street spokesman said: "There is no change to our position. We are not considering an extension to article 50 and are committed to doing whatever it takes to have the statute books ready for when we leave the EU on March 29th this year."
Ms Leadsom, who is in charge of timetabling government business in the Commons, said: "We can get the legislation through and I think we do, in spite of everything, have a very strong relationship with our EU friends and neighbours and I am absolutely certain that if we needed a couple of extra weeks or something then that would be feasible."
In answer to the suggestion that this would amount to an extension of Article 50, which is due to conclude on 29 March, she said: "It doesn't necessarily mean that. I think we would want to think carefully about it. But as things stand I do feel that we can get, with the support of both Houses - the House of Commons and the House of Lords - with goodwill and a determination we can still get the legislation through in good time."
In the interview, Ms Leadsom highlighted tensions when she was asked about cabinet discipline, after the warnings from Ms Rudd and Mr Hammond about the dangers of a no deal Brexit.
"I'm totally aligned to the prime minister," she said. "I believe that is where collective responsibility should lie.
"So number one, the legal default is we leave the EU on 29 March without a deal, unless there is a deal in place. That hasn't changed. That is the prime minister's view and that's my view.
"Of course, it is also very important that we continue to prepare for all eventualities because we do need to make sure that in all circumstances the UK can continue to thrive and do well in a post EU environment.
"I do encourage my colleagues in cabinet to get behind that sentiment and to make sure that we are all on the same page. We are now in the really final days."
Ms Leadsom was highly critical of the the EU for failing to understand the deep unease in the UK over the Northern Ireland backstop.
In the most contentious area of the deal, the UK and the EU have agreed to avoid a hard border between Northern Ireland and Ireland by binding the former closely to EU rules.
This would apply after the transition period if the UK and the EU have failed to negotiate a future relationship by then.
"Keeping the UK in an unlimited, in time terms, backstop that we can't unilaterally exit from under any circumstances is a real problem for many," she said.
"Resolve that and [many Conservative MPs and the DUP] can support the prime minister's deal.
"The EU need to be listening very carefully to that. They are slightly in denial saying that that is not the issue. It very much is the issue.
"So I am hoping the European Commissioners will look very closely at the backstop and think of a way through this, because the legal default is that we leave the EU on 29 March without a deal unless we can agree a deal."
Ms Leadsom was speaking to Newsnight during a visit to Manchester to highlight her work chairing a cross-government group on early years intervention.
You can watch Newsnight on BBC 2 weekdays 22:30 or on iPlayer. Subscribe to the programme on YouTube or follow them on Twitter.

Speaker John Bercow has described the abuse and harassment of MPs outside Parliament as "a type of fascism" and called for a change of policing policy.
He said recent incidents, including Tory MP Anna Soubry being verbally abused on Monday, were "intolerable".
At least 115 MPs have called on police to improve their response to abusive protesters outside Parliament.
The Metropolitan Police has said it is ready to "deal robustly" with any instances of criminal harassment.
Deputy Assistant Commissioner Laurence Taylor said the force was assessing whether any crimes had been committed, following a third-party report of a public order offence on College Green, opposite the Houses of Parliament.
He said Scotland Yard will be "enhancing the policing presence" in the run-up to next week's vote on Theresa May's Brexit deal.
Revised advice was issued to MPs by Parliament security on Tuesday.
Meanwhile, a man has been arrested on suspicion of trespassing after he tried to get into Parliament.
Armed officers arrested him at about 19:20 GMT on Tuesday after he got through Carriage Gates, at the entrance to the Houses of Parliament. He was taken to a police station, the Metropolitan Police said.
The incident is not being treated as terror-related.
The BBC has no plans to stop broadcasting from College Green but does not intend to report from there every day.
A BBC spokeswoman said: "We are working closely with authorities and other broadcasters to ensure the safety of our reporters and interviewees at all times."
Ms Soubry was shouted at - including being called a liar and a Nazi - during live TV interviews on BBC News and Sky.
The former minister - a supporter of a fresh Brexit referendum - was later called "scum" and jostled as she tried to re-enter the Palace of Westminster.
She criticised police for not intervening and called for the protesters to be prosecuted under public order laws.
Section 5 of the 1986 Public Order Act means that "threatening or abusive words or behaviour, or disorderly behaviour" might be deemed a criminal offence.
But Article 10 (right to freedom of expression) and Article 11 (right to freedom of peaceful assembly and to freedom of association) of the European Convention on Human Rights contain the rights to peaceful protest.
College Green is regularly used by media to interview politicians, as well as being a popular site for protesters to gather.
Ms Soubry told the BBC she had "no problem with people protesting", saying this was a "very small group of far-right extremists who just want to undermine democracy".
The MP for Broxtowe said: "There is a very clear distinction between peaceful, lawful protest and robust debate - holding MPs to account, and it can be face to face - and some of the scenes we have seen in the last six weeks here at Parliament."
The cross-party group of MPs who have signed the letter - which includes those both for and against Brexit - said many of the concerns had been "repeatedly raised" with officers and senior policing staff.
"We write to express our serious concerns about the deteriorating public order and security situation in and around the exterior of the Parliamentary estate including College Green," the letter, co-ordinated by Labour MP Stephen Doughty, read.
"After months of peaceful and calm protests by groups representing a range of political views on Brexit, an ugly element of individuals with strong far-right and extreme right connections - which your officers are well aware of - have increasingly engaged in intimidatory and potentially criminal acts targeting Members of Parliament, journalists, activists and members of the public."
The letter said there appeared to be a "lack of co-ordination in the response from the police and appropriate authorities".
Sky News presenter Kay Burley said the "increasingly vile, aggressive and intimidating" abuse had forced her to change her own route to Parliament and she now had to have security protection.
She told BBC Radio 5 Live she had been interviewed three times by the police about the situation, but the protesters knew their rights and what they could and couldn't get away with.
But she added: "How far does it have to escalate before the police have to take it seriously?"
Labour's Mary Creagh said the "really vile, misogynistic thuggery" that had been seen was not an isolated incident.
She pointed to the murder of MP Jo Cox, who was killed in her West Yorkshire constituency by right-wing extremist Thomas Mair in June 2016.
Commons Speaker John Bercow said he was "concerned" about a "pattern of protest" targeting female MPs and journalists and called it a "type of fascism".
In his letter to the Met Police chief on Tuesday, he said he recognised it was "a difficult job striking the balance between allowing peaceful protests and intervening when things turn sour".
But he added: "It's one thing demonstrating from a distance with placards, or calling out slogans - and another, where the protester invades the personal space of a member, subjects him or her to a tirade of menacing, racist, sexist and misogynistic abuse, and follows them back to their place of work."
Labour MP Jess Phillips, who has previously spoken out against online abuse, told the BBC's Victoria Derbyshire programme that some protesters were "organised right-wing groups" trying to "scare our politicians into making decisions based on fringe views".
"People deserve to be safe at work," the Birmingham Yardley MP said. "I didn't come here to be bullied by far-right bullies, far-left bullies, or anyone, we came here to do what we felt was best."
Also on Monday, political commentator Owen Jones published a video on Twitter that he had recorded while being followed and shouted at by a group of protesters outside Parliament.
Last month, a video emerged of prominent Brexiteer Michael Gove being accosted by a protester dressed as Santa as he walked to Parliament.
Mr Bercow said he was aware of protests in recent weeks around the Palace of Westminster "involving aggressive and threatening behaviour towards members by assorted groups that have donned the yellow vests seen in France" - a reference to last year's "gilet jaune" anti-government demonstrations.
By Dominic Casciani, BBC home affairs correspondent
A recognisable figure in the group that surrounded Anna Soubry on Monday is online far-right campaigner James Goddard.
He says there can be no peace while Islam exists in the West and that the establishment is riven with paedophiles. He told police outside Parliament they were "fair game" and "if you want a war, we will give you a war".
Mr Goddard emerged as a DIY far-right campaigner last year as he began to gather followers after campaigning in support of the then-jailed anti-Islam activist, Stephen Lennon aka Tommy Robinson.
Before the incident at Parliament involving Ms Soubry, he'd been helping to organise France-style "yellow vest" protests - including attempts to block bridges in London.
Mr Goddard relies on donations from his followers - he frequently runs crowdfunding appeals for his campaigns.
On Tuesday evening, Facebook confirmed it has closed his account.
"We will not tolerate hate speech on Facebook which creates an environment of intimidation and which may provoke real-world violence," said a spokesman. Minutes later, his separate Paypal crowdfunding page disappeared too.
No 10 said the incident was "unacceptable" and MPs "should be free to do their jobs without any form of intimidation".
The BBC and other broadcasters have set up temporary studios on College Green ahead of the Commons vote on Mrs May's Brexit deal on 15 January.
The BBC's assistant political editor Norman Smith said some MPs had expressed unease privately about being interviewed there, given the frequency and vehemence of the protests.

Thousands of protesters have taken to the streets of central London in a march against Brexit and Conservative Party leadership hopeful Boris Johnson.
The pro-European March for Change is holding a "No to Boris, Yes to Europe" event, and includes a blimp depicting him.
Campaigners are asking for Mr Johnson to "stop the Brexit chaos".
Either he or Jeremy Hunt will be named as Theresa May's replacement as prime minister next week.
Former foreign secretary Mr Johnson, who has declined to comment on the march, is seen as the frontrunner in the contest.
He said the UK would leave the European Union by 31 October "come what may" under his tenure, while Mr Hunt said he expected this to happen by Christmas.
Mr Johnson has claimed Brexit "done right" could "cement and intensify" the union between the UK nations.
The balloon depicting Mr Johnson has "£350m" emblazed on its front, symbolising the leave campaign's pledge of money towards the NHS during the 2016 referendum.
The March for Change organisers said: "We won't put up with a hard Brexit PM being imposed on the country and hurtling us towards the cliff edge."
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As so often, the cabinet managed to agree on what they don't like - the EU's version of the backstop - but they had a harder time agreeing what they do all like.
And even after more than two hours of talks, there is, as things stand, no "fully formed" UK proposal to get the Brexit talks going again.
There is no miraculous solution that can show the EU that promising a customs union to the whole of the UK can have a time limit that fits with their principles.
Donald Tusk has demanded new facts on Wednesday.
But as Theresa May prepares to go to Brussels, there's no sign of them. And there is no deal on the table right now that would definitely get through Parliament.
What to do then when there isn't agreement? Delay of course!
One insider says the government has no choice but to play it long, in the hope that the passage of time will concentrate minds.
Indications from ministers are that the government is now realistically looking to the deal not being done (if it is) until December. (Meaningful vote with your Christmas turkey anyone?)
One cabinet minister told me the PM was trying to manage expectations, telling colleagues today "not to be downhearted" if there was no summit in November.
And there have been suggestions too for ages that the EU would be ready to offer an extension to the whole process.
It's not clear, however, what facts more time would change. Remember a lot of smart people have been trying to find a way to answer all the conundrums for months and months and months.
Officials on both sides thought they were moving towards a possible arrangement of paragraphs last week but the politics here meant it couldn't be done.
And without new facts, will Theresa May be able to buy herself more time? The first call on that will be made in the next 48 hours by the EU.
The worst case scenario for No 10 is that EU leaders are so fed up with the UK position and what they see as the lack of reality, that on Thursday they formally say they will hold a no-deal summit in November.
That would switch them on to a track that would be hard to get off once in motion. One EU source expressed disbelief that Theresa May thought she could turn up on Wednesday with nothing new. It was simply crazy, in their view, to suggest that the ball can be lobbed back into the EU court.
The best case, and it seems right now unlikely, dream scenario is for the EU to say that, after all, there is a deal in reach, so let's get a date in the diary for the sign-off next month.
What seems more likely is a holding position. EU leaders could give some kind of vague noises that both sides still want to pursue negotiations, so that the talks can get going again.
One Brussels source said that while it is "time for choices", they could give the prime minister space and time to build a majority at home for  a deal.
But her party might not. Even if the EU gives her another few weeks to keep going, another few weeks to find a solution, if this summit goes visibly badly, it is not clear that her backbenchers and the Democratic Unionists will back Theresa May to carry on.
It's becoming increasingly common around Westminster to hear MPs say, "I simply can't see a way through."

Is there a conspiracy between so called "disaster capitalists" who have made big financial bets which will come good if the UK leaves the EU without a deal - and a government that is determined to leave on 31 October - do or die?
There has been a lot speculation, that er… speculators who help fund the Conservative Party are set to win big on their bets against the pound and UK assets if the UK leaves the EU without a deal.
The current strain of this theory runs something like this - you Conservatives deliver a no-deal Brexit from which we will profit and we promise to bankroll the party in the coming election and beyond.
There are always plenty of fans of compelling and dramatic narratives like this - but they don't usually include the former chancellor of the exchequer and the former permanent secretary to the treasury - Nick (now Lord) Macpherson.
Philip Hammond said: "Johnson is backed by speculators who have bet billions on a hard Brexit - and there is only one option that works for them: a crash-out no-deal that sends the currency tumbling and inflation soaring."
Lord Macpherson then backed him in the following tweet.
Boris Johnson's own sister Rachel, when trying to explain her brother's do or die approach to leaving on 31 October, said one explanation could be influence "from people who have invested billions shorting the pound and the country in the hope of a no deal Brexit".
What should we make of the clear implication/insinuation that Boris Johnson is being influenced by financial gamblers who stand to make a packet out of no deal?
What we know to be true is that Tory party finances which had begun to struggle under Theresa May are reported to have bounced back under Boris Johnson.
John McDonnell claimed in the House of Commons that backers of no deal had donated £726,000 this year alone - some from hedge funds.
But most of it was not from hedge funds and to put the sums in context, in the first six months of the year, donations to the Tory party totalled more than £9m.
Party officials say the recent uptick in donations is because Johnson is better at shaking the hat - not because he's agreed to seek no deal to enrich a small minority of donors.
The claim that these no deal-backing hedge funds are betting against British companies that will falter come 1 November is also hard to find evidence for. The way most hedge funds work is that they take two positions - one long, one short.
For example, if you think, say, Barclays will do better than, say, Metro Bank over the next few months or years, you back Barclays and you bet against Metro. You make money as long as Barclays goes up more than Metro OR - if they both fall - that Barclays falls less than Metro Bank.
This is not a bet against British banks - it's a bet on two companies' relative performance.
As for the currency, companies of all types make bets against the pound for different reasons. The main reason is as a form of insurance. If I am a US-based multinational that makes, say, 30% of my money in sterling, that contribution will be hit if the pound falls (as most expect will happen after a no-deal Brexit). By taking a bet against sterling, that hit will be offset by the return on that bet and my income will be insured.
But there are hedge funds who place out-and-out bets on currencies. One of them is run by Crispin Odey who made £300m when the pound plunged following the UK referendum result in 2016. He is a no-deal backer, doesn't deny he will prosper if that happens, and contributed £10,000 towards Boris Johnson's campaign.
He described claims that he was trying to influence Johnson as nonsense, insisting he had absolutely no influence over Johnson.
Another hedge fund boss who wished to remain anonymous said the idea that a small group of financiers was pulling the strings to achieve a no deal was ridiculous. Not least, he said, because it would be "bonkers" to bet that a currency that was already at a 30-year low against the rest of the world would go that much lower.
"Most hedge funds are waiting for the moment to buy," he told me, adding that he was certain that Johnson was sincere in his wish for a deal.
They would say that wouldn't they, I hear you say. But it's also worth remembering that for every person who has bet against the pound, there is someone who has taken the other side of that bet. These are usually big international investment banks, the bosses and partners of which often make political donations of their own.
Hedge funds make money by betting the market is wrong - that the price of something is not reflecting what is really going on. It's no secret that many pollsters are hired by hedge funds to conduct political research on which they bet. Paying for better information is not the same as nobbling the result.
The general unease about speculators getting involved in politics is understandable.
As one bank chairman told me: "When hedge fund owners start backing individuals or parties we should worry. It creates at best a perception of conflict of interest. At worst a genuine conflict."
The widespread acceptance of this current conspiracy theory demonstrates that this rings true for many. But, as yet, there has not been enough evidence produced that a few shadowy financiers are pulling the strings of a no-deal Brexit puppet.

The deal the UK government was set to agree with the European Union on Monday came as "a big shock" to the DUP, its leader Arlene Foster has said.
She was speaking to Republic of Ireland national broadcaster RTÉ.
Talks in Brussels halted because the DUP, which props up the Tory minority government, rejected a proposal about the future of the Irish border.
Mrs Foster said the DUP saw the text of the deal on Monday morning, despite asking to see it for five weeks.
"Once we saw the text, we knew it was not going to be acceptable," she said.
Talks between Prime Minister Theresa May and European Commission President Jean-Claude Juncker broke up without agreement on Monday.
The crucial sticking point was over how closely aligned Northern Ireland's regulations will be with those in the Republic of Ireland, and the rest of the EU, in order to avoid a "hard" border.
Mrs Foster said her party could not sign up to anything that would allow a border to develop in the Irish Sea and that its red line was any situation where Northern Ireland was different from the rest of the UK.
Ms Foster also said that the British negotiating team indicated to her that it was the Irish government that prevented the DUP from being shown a copy of the text.
However, the Irish government has rejected Ms Foster's claim and said it had "no role whatsoever in the negotiations conducted by the British government".
"It therefore had no involvement in any decision on which documents should go to the DUP," the Irish government said.
Ms Foster also said that she told Mrs May the DUP would not support Brexit legislation in the House of Commons unless the text presented on Monday was changed.
She said that she had a very open conversation with Mrs May after she had made the DUP position clear in a press conference on Monday afternoon.
She said she told Mrs May that "it could have been dealt with differently".
She said the DUP now wishes to look at the text, make it clear what they cannot agree with and try to work through to move on to Phase Two of the talks.
"Nobody wants a hard border on the island of Ireland," she added.
Taoiseach (Irish prime minister) Leo Varadkar  told the Dáil (Irish parliament) that "the ball is now in London's court".
He said that he accepted that Mrs May was negotiating in good faith but had difficulties.
Earlier on Tuesday, DUP deputy leader Nigel Dodds said the Irish government was risking Anglo-Irish relations and co-operation in Northern Ireland with a "reckless and dangerous" attitude to Brexit talks.
Mr Dodds accused the Irish government of "flexing their muscles".
Speaking in the House of Commons Brexit Secretary David Davis told MPs that Northern Ireland would not be "left behind".
He emphatically denied a suggestion that Northern Ireland would remain in the single market and the customs union after Brexit.
The Labour Party described the government's approach to Brexit talks as "embarrassing".
However, Mr Dodds accused the Irish government of a "noticeable change in tone and aggression" since Mr Varadkar and Irish Foreign Minister Simon Coveney came to power.
by Mark Devenport, BBC News NI political editor
"Rubbish" - the response from a senior DUP source when I put it to them that the party had been kept in the loop about Theresa May's Brexit deal, but got cold feet when the likes of Nicola Sturgeon, Carwyn Jones and Sadiq Khan started demanding the same special treatment for Scotland, Wales and London.
Something doesn't add up.
Last Thursday, DUP leader Arlene Foster declared that her party was "in constant contact on these issues with the government".
Was that via face-to-face meetings of the two parties' "co-ordination committee", or just via telephone conversations? If the latter, the line must have been very crackly.
Mr Dodds added it was clear that the European Union has given a veto to the Irish government and that they were "flexing their muscles and using their current position to try and gain wins for them".
"I don't argue with their desire to advance their interests but they're doing so in a reckless and dangerous way that is putting at risk years of good Anglo-Irish relations and good co-operation within Northern Ireland."
He added: "What matters are the words that are used in text and in international treaties and agreements and it's vitally important that text translates accurately to what are the general principles of political agreement."
The prime minister needs the support of the DUP, which is Northern Ireland's largest party and has 10 MPs at Westminster, because she does not have a majority to win votes in the House of Commons.
Meanwhile, Shadow Brexit Secretary Keir Starmer claimed in the House of Commons that the Conservatives' agreement with the DUP at Westminster was a "coalition of chaos" and said "the DUP tail is wagging the Tory dog."
But Mr Davis said "the suggestion that we might depart the European Union to leave one part of the United Kingdom behind and still inside the single market and the customs union - that is emphatically not something that the UK government is considering".
"So when the first minister of Wales complains about it or the first minister of Scotland uses it as a reason to start banging the tattered drum of independence or the Mayor of London says it justifies a hard border on the M25, I say they are making a foolish mistake.
"No UK government would allow such a thing let alone a Conservative and Unionist government."

Universities and Science Minister Chris Skidmore has said that the UK will not implement the EU Copyright Directive after the country leaves the EU.
Several companies have criticised the law, which would hold them accountable for not removing copyrighted content uploaded by users, if it is passed.
EU member states have until 7 June 2021 to implement the new reforms, but the UK will have left the EU by then.
The UK was among 19 nations that initially supported the law.
That was in its final European Council vote in April 2019.
Copyright is the legal right that allows an artist to protect how their original work is used.
The EU Copyright Directive that covers how "online content-sharing services" should deal with copyright-protected content, such as television programmes and movies.
It refers to services that primarily exist to give the public access to "protected works or other protected subject-matter uploaded by its users", such as Soundcloud, Dailymotion and YouTube.
It was Article 13 which prompted fears over the future of memes and GIFs - stills, animated or short video clips that go viral - since they mainly rely on copyrighted scenes from TV and film.
Critics claimed Article 13 would make it nearly impossible to upload even the tiniest part of a copyrighted work to Facebook, YouTube, or any other site.
However, specific tweaks to the law in 2019 made memes safe "for purposes of quotation, criticism, review, caricature, parody and pastiche".
Prime Minister Boris Johnson criticised the law in March, claiming that it was "terrible for the internet".
Google had campaigned fiercely against the changes, arguing they would "harm Europe's creative and digital industries" and "change the web as we know it".
YouTube boss Susan Wojcicki had also warned that users in the EU could be cut off from the video platform.
Kathy Berry, a professional support lawyer at Linklaters, welcomed the government's stance on the law, claiming it will "allow the UK to agree to more tech-friendly copyright provisions in free trade deals with other countries".
The law sparked suggestions from its biggest critics that it would end up "killing memes and parodies," despite it permitting the sharing of memes and GIFs.

The Welsh Assembly does not have a legal right to be consulted by UK ministers triggering Brexit, the Supreme Court has ruled.
Senior judges said that the UK government cannot start Article 50 without consulting MPs.
They said assembly members have no veto over the process to leave the EU.
But the Welsh Government's chief legal officer Mick Antoniw called the ruling "a victory" in upholding the sovereignty of Parliament.
Welsh ministers had argued that the assembly should be consulted on starting Brexit. They had intervened in the UK government appeal against an earlier High Court ruling.
Counsel General Mr Antoniw told the assembly on Tuesday that AMs are likely to vote on Brexit, despite the ruling, although he said it was not a veto.
Giving the judgement on Tuesday, President of the Supreme Court Lord Neuberger said: "On the devolution issues, the court unanimously rules that UK ministers are not legally compelled to consult the devolved legislatures before triggering Article 50.
"The devolution statutes were enacted on the assumption that the UK would be a member of the EU, but they do not require it.
"Relations with the EU are a matter for the UK government."
The ruling said the assembly and other devolved legislatures had no veto.
But it did say withdrawal from the EU will change the powers of the governments and assemblies in Wales, Scotland and Northern Ireland.
The Welsh Government had argued that if MPs did not vote on Article 50, which was the UK government's original intention, it would undermine the basis for devolution.
Welsh ministers had also argued that this plan would have short-circuited a convention which requires Welsh assembly members to vote on legislation which affects the Welsh devolution settlement.
The Sewel Convention is an arrangement between the UK and Welsh governments where if any new laws come in that affect devolution, they have to be approved by AMs by a vote.
But the Supreme Court ruling sets out that Sewel is a political convention and not a legal one, and so is not a legally enforceable obligation.
The assembly research service states the court is not giving the UK government and Parliament license to ignore Sewel, but it cannot decide disputes about whether it had been applied correctly.
Mr Antoniw, Welsh Government's senior legal advisor and am AM, told BBC Wales the ruling was "certainly a victory in terms of upholding the sovereignty of Parliament".
"We've never argued for a veto, and the court made that point, but what it does do is stress the importance of the Sewel Convention in terms of engagement."
Earlier, speaking to BBC Radio Wales before the judgement, Mr Antoniw defended the £84,000 cost of the Welsh Government's intervention, saying: "The voice of Wales within the UK constitution is priceless."
Plaid Cymru spokesman for external affairs Steffan Lewis said the party would still seek to table a vote in the assembly on the triggering of Article 50.
"It is a simple matter of democracy that the devolved legislatures should have a role in commencing the process of leaving the EU," he said.
UKIP MEP and independent AM Nathan Gill said the Brexit white paper published by the Welsh Government on Monday "will make it into the Guinness Book of Records for having the shortest shelf life ever, 24 hours".
"Because it's now been made obsolete," he claimed.
But Mr Gill - a member of the committee advising First Minister Carwyn Jones on Brexit - said the Supreme Court judgement in favour of parliament was "no surprise".
An UKIP assembly group spokesman said it welcomed the judgement on Article 50 and Parliament, and that any attempt to block Brexit would trigger an immediate general election: "We say bring it on."
"It would be absurd for Wales, Scotland, Northern Ireland to have a veto over triggering Article 50," he said.
The Welsh Conservatives' Europe spokesman Mark Isherwood, said: "The Welsh Government's tortuous arguments were an expensive sideshow.
"It would have been better if every effort had been focused on delivering a Welsh Government paper on Brexit before the UK government announced its negotiating strategy."
Welsh Liberal Democrat leader Mark Williams welcomed the ruling, saying it showed the sovereignty of parliament was paramount, and that his party will vote against Article 50.
Several Labour MPs have indicated they will disobey any order by party leader Jeremy Corbyn to vote in favour of Article 50.
Pontypridd MP Owen Smith, who backed Remain, suggested there ought to be a fresh referendum on the terms of leaving the EU, fearing the UK was set for the "hardest of hard Brexits" by leaving the single market and the customs union.
"The right thing to do then is to allow the British people once more in an ultra-democratic moment to confirm whether they really want the hard, hard Brexit they are likely to get," he said.

Labour will not support any Brexit deal negotiated by the government unless it meets the party's "six tests", the shadow Brexit secretary has said.
Any deal must include a strong relationship with the EU and the same benefits the UK currently has from the single market, Sir Keir Starmer said.
The UK should "honour our obligations" regarding any "divorce bill", he added.
The government will trigger Article 50 on Wednesday, kick-starting talks aimed at agreeing a Brexit deal with the EU.
The government will then publish its Great Repeal Bill on Thursday. It will propose giving ministers the powers to change some aspects of European laws when they have been incorporated into UK legislation, without needing the approval of Parliament.
Triggering Article 50 begins a two-year negotiation process to attempt to reach a deal before Britain officially leaves the EU in March 2019.
If no deal is agreed, it would mean World Trade Organization rules would be imposed - less favourable terms than trading within the single market.
Outlining Labour's demands in a speech in London, Sir Keir said the prime minister "should be under no illusion" and added that Labour would not support a deal "that fails to reflect core British values and the six tests I have set out today".
"All of us want the best for Britain. But the stakes are high and the prime minister's approach so far does not bode well," he said.
The BBC's assistant political editor Norman Smith said some of the tests were akin to "motherhood and apple pie" and could be met quite easily.
But he said Labour were setting the bar quite high in calling for the UK to retain the "exact same benefits" as currently afforded by membership of the single market and the customs union.
In demanding this, Sir Keir said Labour was only seeking the same objective that Brexit Secretary David Davis had set himself in Parliament.
"The government can't turn around and say this is unachievable because it was David Davis... who said that," he said.
Another key demand is for "fair management of migration in the interests of the economy and communities".
Sir Keir said he accepted that the EU principle of freedom of movement "has to go" but he insisted a future immigration policy must be one of managed migration which works for businesses and communities.
One of the tests calls for "a strong collaborative future relationship with the EU". He said it was important to state that because "some of the pure Brexiteers actually want us to crash out [without a deal], either at the Article 50 stage in two years or before that".
"This is the worst of all possible outcomes," he added, saying there would be greater certainty if Theresa May agreed to transitional arrangements from 29 March 2019 until a treaty setting out future relations was finally signed.
Responding to Sir Keir's intervention, Conservative MP Maria Caulfield said Labour were divided over the UK's future outside of the EU and merely "sniping from the sidelines".
"They can't even agree on whether they want to control immigration, and have today failed to make ending uncontrolled free movement one of their tests for supporting a deal with the EU," she said.
No 10 said it wanted the "greatest possible access" to the single market.
European Commission President Jean-Claude Juncker suggested last week that the UK may have to pay up to £50bn for privileged access to the single market and customs union.
Asked about this on Sunday, Home Secretary Amber Rudd said business wanted the "widest possible access" to the single market but how much this would cost would form part of the negotiations.
She also dismissed a "no deal" scenario outlined by EU Brexit negotiator Michel Barnier - with truck queues at Dover, disruption to air traffic and a suspension in the movement of nuclear materials to the UK - as "apocalyptic".
"I think it's fair to say I don't recognise that description... he would say that wouldn't he?" she said.
It has been reported the Great Repeal Bill will include proposals for the government to be given a "new time-limited correcting power" which would allow changes to be made through so-called Henry VIII clauses - without needing the approval of Parliament.
The government says it needs the power to make "technical" changes quickly as a lot of EU law will not work properly without changes being made but Labour leader Jeremy Corbyn says he will not allow Parliament to be "overridden" and ministers to issue a "series of diktats".
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If you walk down Whitehall in central London, you cannot escape reminders of wars fought and empires run from this small district on the north bank of the Thames. There are memorials to the fallen, statues of field marshals and even a Turkish cannon captured in some long-forgotten conflict.
Yet the civil service that once gloried in its global administrative stretch is now the smallest it has been since World War Two. And with the government launching the British state on its greatest administrative, economic and legal reform since it committed the nation to total war in 1939, there is a simple question: is Whitehall up for Brexit?
"It's been a scramble but the ducks are in a row," one Cabinet minister told me confidently.
For the scale of the challenge is immense.
Thousands of civil servants to be mobilised and retasked, thousands of laws and regulations to be rewritten or rejected and thousands of people trained and employed to do the many things currently carried out by the European Union.
This endeavour is not only about the two years of initial negotiations with 27 EU member states that will shortly begin, it is also about the mammoth preparations the UK must make for leaving the EU whatever the outcome of the negotiations.
"The challenge of Brexit has few, if any, parallels in its complexity," says Sir Jeremy Heywood, the Cabinet Secretary. "Its full implications and impact on the political, economic and social life of the country... will probably only become clear from the perspective of future decades."
Perhaps the greatest challenge the civil service has faced was its utter lack of preparation for the British people voting out in the referendum last June. They were expressly forbidden from drawing up any plans by David Cameron's administration and have been playing catch up ever since.
Ministers say the civil service has responded well, creating two new government departments from a standing start. The Department for Exiting the EU (DExEU) has something north of 320 staff, the Department for International Trade, several thousand.
Both departments, along with the Foreign Office, have been given an extra £400m by the Treasury over the next four years to pay for their work on Brexit. There were some initial turf wars but officials now say there is greater singularity of purpose.
Much work has been done analysing options, quantifying markets and assessing laws. Huge volumes of paper have been landing on DExEU desks looking at the impact of Brexit on every aspect of the economy.
The aim is to allow David Davis, the Secretary of State for Exiting the EU, to draw up an a la carte menu for the prime minister, setting out potential options and costs so that she can navigate the negotiations ahead.
For there is no doubt that these will be Theresa May's negotiations. The main negotiating team will include Mr Davis, his permanent secretary, Olly Robbins, and Sir Tim Barrow, the UK permanent representative to the EU.
Below them will be civil servants from all affected government departments, summoned in to work on specific "chapters" of the negotiations, on everything from fish to agriculture to financial services. They will be the team dealing with the European Commission negotiators on an almost daily basis.
Yet above them will be Mrs May who will have to drive the talks and make the big calls. But such is the size of the task that even the prime minister will struggle to retain her usual iron grip.
One minister told me: "This is the first big test to see if she can delegate. This is so big that No 10 cannot control it, they cannot be on top of all the detail."
Not all are so sanguine about the preparedness of Whitehall. The National Audit Office says in a new report that, while 1,000 new roles have been created in the civil service to deal with Brexit, a third remain unfilled and most of the new appointees have simply been transferred from other parts of government.
And the Institute for Government warns that departments such as the Home Office and the Department for Environment, Food and Rural Affairs are underfunded, cannot afford more staff and will be forced to drop non-Brexit work.
Other insiders warn that, although much work has been done setting out options, less thought has been devoted to how the negotiations will progress themselves and how the government should organise itself. Officials talk of not knowing precisely for what they are preparing because Downing Street refuses to reveal its negotiating plans.
The process, inevitably, will begin with negotiations about the negotiations. Who will talk to whom, about what and in what order? The UK government wants to discuss its divorce from the EU at the same time as its future trade relationship. The EU says the two issues must remain separate.
Then will come the exit agreement itself. Much will be visceral and hard-fought. Protecting the rights of EU nationals in the UK and vice versa sounds easy as both sides say they want this to be resolved early on and want to keep the status quo. But the hugely complex detail will be hard to agree.
Yet sorting that out might be easy compared to agreeing how much money, if any, the UK will owe the EU when it leaves. The government says nothing, the EU is hinting at £50bn. And all this is before any negotiations about any future trade arrangement between the UK and the EU and any transitional process that may be needed.
While this will generate a huge amount of work for some in the civil service, many other officials will be focused instead on preparing the UK for leaving the EU come what may.
Much of this will focus on Westminster. There is the Great Repeal Bill to be written and passed through Parliament to ensure that all EU law is transferred automatically into UK law the moment we leave. The aim is to ensure there is no legal chaos and to allow Parliament all the time it needs gradually to unstitch the UK from four decades of EU legislation.
This will be a massive piece of legislative work that will require officials to re-examine huge swathes of UK law. They will have to decide which bits of EU law to return to Westminster and which bits are devolved, a tricky issue in light of Holyrood's demand for a second independence referendum. The Institute for Government warns there might be a need for further 15 separate Brexit Bills.
In the short term, there are a huge number of separate parliamentary inquiries into Brexit - 55 in all - being carried out by various committees of MPs and peers. Ministers have to reply to each one within 60 days and officials are struggling to meet that deadline.
Then there is the process of the UK re-establishing its status at the World Trade Organization (WTO), something that will be needed even if we get a new trade deal with the EU.
The government hopes to transfer its current EU tariff rates into a new UK-specific schedule of trade commitments. But such a "copy and paste" arrangement will be complicated and will almost certainly face challenge from other WTO members. UK diplomats in Geneva, where the WTO is based, have a hard job of reassurance ahead of them.
And then there is also the process of creating new organisations that will fill the gaps in our national life left as the EU tide ebbs from our shores. Officials will need to set up new customs and immigration systems, neither of which will be simple or easy.
So, as the phoney war ends with the triggering of Article 50, Whitehall is facing perhaps its greatest challenge in a generation.

The UK should be able to unilaterally cancel its withdrawal from the EU, according to a top European law officer.
The non-binding opinion was delivered by an advocate general of the European Court of Justice.
A group of Scottish politicians has asked the court whether the UK can call off Brexit without the consent of other member states.
The Court of Justice (ECJ) will deliver its final ruling at a later date.
The advice from advocate general Manuel Campos Sanchez-Bordona comes as the House of Commons begins five days of debates on Prime Minister Theresa May's proposed Brexit deal, with a vote due to be held next Tuesday.
In a written statement, the ECJ said Mr Campos Sanchez-Bordona's opinion was that if a country decided to leave the EU, it should also have the power to change its mind during the two-year exit process specified in Article 50 of the EU treaty.
And it should be able to do so without needing the consent of the other 27 member states - contrary to what the EU itself has argued.
While the advocate general's opinions are not binding, the court tends to follow them in the majority of its final rulings.
The anti-Brexit politicians and campaigners who have brought the case hope it will give MPs an extra option when considering whether to approve Mrs May's draft deal or not, because it could keep alive the prospect of calling off Brexit - potentially through another referendum.
The ECJ statement said the advocate general had proposed that the Court of Justice should "declare that Article 50 allows the unilateral revocation of the notification of the intention to withdraw from the EU".
It added: "That possibility continues to exist until such time as the withdrawal agreement is formally concluded."
The UK is due to leave the EU on 29 March next year, but the deal negotiated with the EU has to be backed by a majority MPs if it is to come into force.
Welcoming the advocate general's opinion, SNP MEP Alyn Smith, one of those who brought the case, said it showed that "we now have a roadmap out of the Brexit shambles".
He said parliament was not necessarily facing a choice between accepting Mrs May's deal or leaving the EU with no deal, and that "there are other options, and we can stop the clock."
A cross-party group of politicians and campaigners including Green MSPs Andy Wightman and Ross Greer, MEP Alyn Smith and MP Joanna Cherry of the SNP, and Labour MEPs David Martin and Catherine Stihler brought the case together with lawyer Jolyon Maugham QC, director of the Good Law Project.
They initially took it to the Court of Session in Edinburgh, which ultimately agreed to pass it to the ECJ.
Two attempts by the UK government to appeal against the referral to the European court were rejected, and the case was opposed by the government and the EU institutions in a hearing before all 27 ECJ judges last week.
Hubert Legal, the chief lawyer for the European Council, argued that allowing unilateral withdrawal could create "endless uncertainty" by allowing countries to announce they are leaving the EU in an attempt to secure better membership terms, before cancelling their withdrawal.
The UK government's lawyers argued that the case was purely hypothetical as "the UK does not intend to revoke its notification", and ECJ judges should therefore refuse to rule on it.
They added that the politicians behind the case wanted to use it as "political ammunition to be used in, and to pressure, the UK parliament".
The advocate general's opinion that the UK has the right to unilaterally withdraw Article 50 notification of its intention to leave the EU flies in the face of what the UK government and the EU want.
Although the Advocate General's opinion is non-binding, the ECJ follow his opinions in the majority of cases.
The whole issue of revocation remains hypothetical at present because the government has made it clear there is no possibility of seeking to revoke the notice to leave the EU.
However, the statement raises the question of how the UK might revoke notification.
It would almost certainly need to be done by an act of parliament. If it was done by ministers alone using prerogative powers it would frustrate the will of parliament as expressed in the European Union (Withdrawal) Act 2018.
It should be noted that the statement and the case concerns revocation of notice to leave, and not a delay or extension of the two-year period provided for under Article 50.
That period can be extended, but only with the agreement of all of the other 27 EU states. Whereas extension of the Article 50 period could become a political necessity, revocation of Article 50 remains something of an academic point at present. However, that would change if there was a second referendum in which the British people voted to remain in the EU.

Prime Minister Theresa May is to officially notify the European Union next Wednesday that the UK is leaving.
Downing Street said she would write a letter to the European Council, adding that it hoped negotiations on the terms of exit and future relations could then begin as quickly as possible.
An EU spokesman said it was "ready and waiting" for the letter.
Mrs May's spokesman also rejected reports an early election may be held, saying: "It's not going to happen."
Under the Article 50 process, talks on the terms of exit and future relations are not allowed until the UK formally tells the EU it is leaving.
If all goes according to the two year negotiations allowed for in the official timetable, Brexit should happen in March 2019.
A No 10 spokesman said the UK's Ambassador to the EU, Sir Tim Barrow, informed the European Council, headed by President Donald Tusk, earlier on Monday of the date that Article 50 would be triggered.
Mrs May is expected to make a statement to the House of Commons on Wednesday shortly after invoking Article 50, setting out her aims.
A spokesman said the government wants negotiations to start as soon as possible but added that they "fully appreciate it is right that the other 27 EU states have time to agree their position".
The BBC's Ben Wright said he expected the Article 50 letter to be short, possibly extending to two pages at most, and for Mrs May to use it to publicly reiterate her general objectives - such as leaving the single market but reaching a mutually beneficial agreement on trade and other issues.
Speaking in Swansea on Monday, during the first of a series of visits around the UK before she triggers Article 50, Mrs May said she was intent on "delivering on Brexit and getting the right deal".
Last year's referendum result, she added, "was not just about leaving the EU" but was a vote for a "change in the way the country works".
"Part of that is building a strong economy and ensuring that the benefits of economic growth and prosperity are felt across every part of the UK."
Brexit Secretary David Davis said the UK was now "on the threshold of the most important negotiation for this country for a generation".
"The government is clear in its aims," he said. "A deal that works for every nation and region of the UK and indeed for all of Europe - a new, positive partnership between the UK and our friends and allies in the European Union."
In response to the news, Mr Tusk tweeted: "Within 48 hours of the UK triggering Article 50, I will present the draft Brexit guidelines to the EU27 Member States."
Mr Tusk has previously said he expects to call an extraordinary summit of the 27 other members within four to six weeks, to draw up a mandate for the European Commission's chief negotiator, Michel Barnier. Under this scenario, talks are likely to begin in earnest in May.
Sir Tim Barrow, the UK's most senior representative at the EU, said the 27 had had plenty of time to prepare for this moment and he expected them to set out their stall "pretty quickly".
"Our mandate is clear, it is to get on with it," he told MPs on the European Scrutiny Committee. "There is a timetable that everyone has bought into it."
Mrs May said last year that she intended to notify the EU of the UK's intention to leave by the end of March. The move was approved by Parliament two weeks ago when peers and MPs passed unchanged a bill giving the prime minister the authority to set the process in motion.
EU leaders have said they want to conclude the talks within 18 months to allow the terms of the UK's exit to be ratified by the UK Parliament and the European Parliament, as well as approved by the necessary majority of EU states.
Mrs May has said MPs and peers will have a vote on the deal she negotiates but she has insisted the UK will leave anyway even if Parliament rejects it. The government has said it expects to secure a positive outcome but made clear there is a chance of there being no formal agreement with Mrs May saying no deal was better than a bad deal.
Ahead of Mrs May naming the date European Commission President Jean-Claude Juncker was quoted in German newspaper Bild saying the UK may have to abandon hopes of getting a trade deal if it did not agree to the term offered by the EU.
These terms may include a £50bn "divorce bill" and Mr Juncker said Brexit could bring the remaining 27 members closer together: "They will all see from the UK's example that leaving the EU is a bad idea."
Labour's Keir Starmer said the opposition would hold the government to account throughout the process, claiming the prime minister had failed to provide certainty about her plans or prepare for the "clear dangers" of not reaching a deal at all.
The Scottish National Party's Europe spokesperson at Westminster, Stephen Gethins, said: "Today's announcement... shatters beyond repair any notion or position that the Prime Minister is seeking a UK-wide agreement.
"For nine months since the EU referendum, there has been no attempt by the UK government to seek a meaningful discussion or agreement with the devolved administrations."
Lib Dem leader Tim Farron, who has called for the public to have their say on the terms of exit in a further referendum, said Mrs May's decision to rule out membership of the single market before negotiations began was proof she was pursuing an "extreme and divisive" Brexit.
"Leaving the single market was not on the ballot paper in the referendum, it is a political choice made by Theresa May," he said.
Later this week, EU leaders will gather in Rome to mark the 60th anniversary of the Treaties of Rome, which established the European Economic Community - the initial forerunner to the EU. Mrs May is not attending the event.

Conservative donor Lord Ashcroft says he believes Boris Johnson's Brexit interventions might help Theresa May in her negotiations with the EU.
The former deputy chairman said the PM could tell Brussels: "This is the type of difficulty I have in bringing people into line."
Mr Johnson, the foreign secretary, has been accused of undermining Mrs May by setting out his own vision of Brexit.
But Lord Ashcroft said he could not "see much harm" in his recent comments.
Speaking to BBC political editor Laura Kuenssberg at the Conservative Party conference in Manchester, the tycoon said: "Everyone wants the best deal for Britain in EU negotiations - the issue is that everyone has a different view on how they should proceed.
"But it is a complex set of negotiations and I don't believe that a deal will be struck until much nearer the time and there's a lot of play acting going on and positioning.
"I don't see much harm in what Boris has put forward, I don't see it's highly inconsistent. At the same time Theresa can use that as a strength in the EU negotiations by saying 'this is the type of difference I have in bringing people into line'."
After the Conservatives lost their Commons majority in June's general election, much of the talk at conference is about how to address the challenge posed by Jeremy Corbyn and Labour.
Lord Ashcroft said the party needed to "reassemble" and "get its act together", adding that there would be different "nuances" from ministers throughout the Brexit process.
In his latest comments on Brexit, Mr Johnson wrote in The Sun that Mrs May's planned transition phase must not last "a second more" than two years.
The foreign secretary also set out his plan for Brexit in a Daily Telegraph article last month.
This sparked accusations of "backseat driving" and prompted Mrs May to say the government was "driven from the front".

Austrian chancellor Sebastian Kurz has told Theresa May it is "important to avoid a hard Brexit", after talks with the UK prime minister.
Mrs May is in Salzburg as part of a mission by UK ministers to sell their post-Brexit trade proposals.
Mr Kurz said he viewed Brexit "negatively" but felt negotiations were going "quite well".
Mrs May then held talks with Czech PM Andrej Babis before heading off on her summer holidays.
Speaking at a brief joint press conference, Mr Kurz, who has just assumed the EU presidency for six months, said: "The Brexit decision is a decision we see very negatively.
"But, of course, it has been taken by the British people so now we have to find a way to deal with it, and from our point of view it is important to avoid a hard Brexit."
He said he hoped the UK's talks with EU chief negotiator Michel Barnier would be successful and a "solution" could be found by October.
The BBC understands that Mr Kurz has indicated he supports the idea of EU leaders holding formal Brexit talks at a summit in Salzburg in September.
Mrs May hailed the strength of the UK's relationship with Austria, adding: "We are delivering on a vote of the British people, they chose to leave the EU and we will deliver that."
Later, Mrs May pitched her idea for a post-Brexit free trade area to her Czech counterpart Andrej Babis.
A Downing Street spokesman said: "She highlighted that a UK-EU free trade area would maintain frictionless trade that would enable businesses across Europe to maintain their vital integrated supply chains.
"They agreed it was important to find a solution and that negotiations should continue at pace."
Both the EU and UK say a deal can be done by October - five months before the UK is due to leave the European Union - but have also said preparations are being made in case negotiations end in no deal.
Mr Barnier has already rejected a key element of her proposal for post-Brexit trade with the EU.
International Trade Secretary Liam Fox has accused the EU of pushing the UK towards a "no deal" scenario because they "keep saying no to everything".
Mr Fox, who is on a trade mission to San Francisco, told Business Insider the UK should leave without a deal if talks break down, rather than requesting an extension of the Article 50 process to continue negotiations, as some have suggested.
"To attempt to extend our membership even longer, many voters would regard as a complete betrayal by the political class, and I think they would be right," he added.
Mrs May's trip to Austria is one of several being made to Europe by British government ministers over the summer to promote her plan, detailed in the Brexit White Paper, to European leaders.
Foreign Secretary Jeremy Hunt met his German counterpart in Berlin on Monday and the UK chancellor, home secretary, business secretary and the minister for the Cabinet Office are also meeting counterparts across Europe over the summer.
Following talks in Austria, Mrs May will head to Italy with her husband, Philip, for a week before returning to the UK to work.
She is also due to attend a World War One memorial event marking the centenary of the battle of Amiens, which began on 8 August 1918, before heading off for two weeks' holiday in Switzerland.
Analysis by BBC Diplomatic Correspondent James Robbins
Salzburg in high summer is packed with tourists and music lovers enjoying the annual festival.
Theresa May went to the opera on Friday night, but only after her talks with Mr Kurz and Mr Babis.
The prime minister is hoping to persuade them to urge others in the EU27 to relax their common position - particularly by accepting her proposals for continuing free movement of products after Brexit.
But there's no sign either Austria or the Czech Republic is willing to budge. Eurosceptic feeling may be strong among their populations, but neither leader is contemplating following Britain out of the Union.
Instead, both governments believe Mrs May is still cherry-picking and that Britain must blink first to avoid what they call a catastrophic crash-out they are convinced would hurt the UK far more than the EU.
Mozart's The Magic Flute, in the city of his birth, should have been something of a relief for Mrs May.
The UK's Brexit White Paper, drawn up after agreement with the cabinet at Chequers, proposes close ties in some areas, such as the trade in goods, but Mrs May says it will end free movement of people and the jurisdiction of the European Court, and allow the UK to strike trade deals with other nations.
It would involve the UK collecting some EU tariffs - in a bid to ensure frictionless trade in goods and to avoid a hard border in Northern Ireland - under its proposed Facilitated Customs Arrangement for goods and agri-foods.
The plan sparked two UK cabinet resignations - former Brexit Secretary David Davis and former Foreign Secretary Boris Johnson.
Mr Barnier said on Thursday that the EU "will not delegate the application of its customs policy and rules and VAT and excises duty collection to a non-member who would not be subject to the EU's governance structures".
Any customs arrangement or union "must respect this principle", he said.

At a time of great uncertainty the new chancellor chose to display caution.
Despite long wanting to get his hands on the nation's purse strings, Philip Hammond was not tempted into grand gestures.
There were modest giveaways for those "just about managing" in order to keep true to Theresa May's promise of a Government for all; a reduction in the rate benefits are withdrawn for those working, a ban on letting fees and a boost to the minimum wage - much briefed in advance to perhaps gain some headlines before gloomy forecasts became the story.
There was a shift away from his predecessor's focus on deficit reduction within a set timeframe - instead Mr Hammond said he would deliver a surplus as soon as possible, announcing investment in housing and roads, money for research and development - the focus on boosting productivity.
But this was still a Chancellor keen to limit spending in order to secure stability.
Brexit has made the future unpredictable.
Philip Hammond may have more insight that most into the Government's planned approach to leaving the EU, but he still wanted to ensure he had enough in his back pocket to withstand any shocks that may come.
And with vast increases in borrowing and reduced growth predicted, Mr Hammond limited the giveaways and changed the economic rules to give himself the flexibility to respond.
This was a careful balancing act, an attempt to follow through on promised support for those in society who need it most while keeping the nation's books in order.
At the same time, this was an attempt to recognise the potential economic turbulence Brexit could bring without invoking the ire of backbench Eurosceptics with an overly negative outlook.
Mr Hammond was careful to speak of opportunities as well as challenges, describing a "great nation", resilient and strong.
By his own admission there was no grand "rabbit in the hat". Mr Hammond wasn't out to steal the show, but rather prove he can be the steady hand on the tiller in choppy economic waters.
But for Labour, this was an opportunity to seize on a chink in the government's economic armour, with the Shadow Chancellor John McDonnell saying the much-hailed long term economic plan had been an "abject failure".

Chancellor Philip Hammond has called economic forecasts in the Autumn Statement one of a "range of outcomes" after some pro-Brexit MPs criticised them for being too pessimistic.
The Office for Budget Responsibility (OBR) forecast more government borrowing and reductions in economic growth after the referendum.
Ex-minister Iain Duncan Smith accused the OBR of "utter doom and gloom".
But Mr Chancellor Hammond said it was good to prepare for a "rainy day".
He added that the government was investing to boost infrastructure and economic productivity and there was a "downward path in borrowing".
BBC economics editor Kamal Ahmed said the chancellor "hopes that the forecasts do prove very gloomy" and he was "setting a bottom line from which he hopes the government can clamber upwards".
During Wednesday's Autumn Statement, Mr Hammond's first since becoming chancellor, he told MPs the UK's deficit would no longer be cleared by 2020.
And the OBR estimated the government would have to borrow £122bn more than forecast in March's Budget, with the referendum result accounting for £58.7bn of this.
The Brexit vote meant potential growth in the current Parliament would be 2.4% lower than forecast in March, according to the OBR who also admitted producing a forecast was "far from straightforward", as it had not been given any extra information from the government about its negotiation plans.
It said: "We have made a judgement - consistent with most external studies - that over the time horizon of our forecast any likely Brexit outcome would lead to lower trade flows, lower investment and lower net inward migration than we would otherwise have seen, and hence lower potential output."
The organisation said the economy would be affected by future choices that the government makes about regulatory and other policies and it "could move in either a growth-enhancing or a growth-impeding direction".
Asked about the OBR's predictions, the former Work and Pensions Secretary and Leave campaigner Mr Duncan Smith told the Daily Telegraph it was "another utter doom and gloom scenario" from the organisation.
The Economists for Brexit group predicted more "humiliating U-turns" from the OBR, saying it had  "assumed a pessimistic outlook for the UK economy outside the EU, based on bad economic policy-making".
Conservative MP John Redwood, who also supported Brexit, added: "Their [GDP growth] forecast probably is too low, their borrowing forecast is far too high, and we'll get good access to the single market once we're out of the EU."
But Downing Street dismissed the criticism, saying the OBR's role was to "provide transparency and credibility".
She added: "They are an independent forecaster. We won't get into second guessing them."
In his statement, Mr Hammond promised to invest £23bn on "innovation and infrastructure" over the next five years, with more money for roads, broadband and regional development.
He told BBC Radio 4's Today programme: "There's a downward path in borrowing. We need to keep the downward path on borrowing... But we also need to invest in our economy, to generate the revenue that will drive down the debt."
Describing economic forecasting as "not a precise science", Mr Hammond said of the OBR's forecast: "We should think of it as one of the possible range of outcomes we need to plan for."
He added: "We have a very strong foundation on which to build."
Mr Hammond also said: "We should have a plan which both invests in our economy and puts a little aside for the possibility of a slightly more rainy day next year or the year after."
Uncertainty was "not just about" Brexit but the change of US government when Donald Trump takes office and the growth rate of the Chinese economy, he added.
Labour said the Autumn Statement offered no hope for the future after six "wasted" years.
Among Mr Hammond's announcements were:
The speech also triggered questions about the future of the so-called "triple lock" protection for state pensions, while campaigners criticised the lack of extra funding for social care.
The triple-lock guarantees that state pensions rise by the same as average earnings, the consumer price index, or 2.5%, whichever is the highest.
Mr Hammond said the government would meet this pledge, adding: "But as we look ahead to the next Parliament, we will need to ensure we tackle the challenges of rising longevity and fiscal sustainability."
Former work and pensions secretary Stephen Crabb backed a review of the mechanism after 2020.
He told the BBC: "The fiscal impact of the triple lock is not something anyone can dismiss lightly and if we are serious about ensuring that our welfare system remains affordable in the very long term then my own view is that the triple lock has served its purpose and probably needs to get amended, to ensure that we don't have to keep going back to working age families and squeezing the same people's incomes time and again."
Meanwhile health and social care leaders have condemned the statement for a "missed opportunity" to announce new investment.
For Labour, shadow chancellor John McDonnell told BBC One's Breakfast that although he welcomed the government "moving on investment policy" there had been "mismanagement of the economy over the last six years".
"I find it extremely worrying that they've used the last six years with austerity measures and instead of investing they've been cutting, and as a result of that they're unprepared and ill-equipped for Brexit."
The SNP said Mr Hammond had offered little on Brexit, which it called the "elephant in the room".
Liberal Democrat leader Tim Farron said: "The government's mishandling of Brexit is hitting those on lower and middle incomes the hardest."
He added that "rhetoric" about helping those "just about managing" had not resulted in action, creating "surprising and massive disappointment".
But UKIP said billions were being wasted by the government "delaying" the UK's exit from the EU.
Plaid Cymru said there was little in the statement to help rebuild the Welsh economy and close the wage gap with England.
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The outlook for wages is "dreadful" with the squeeze on pay lasting for more than 10 years, independent economists have said.
The Institute for Fiscal Studies (IFS) said workers would earn less in real wages in 2021 than they did in 2008.
Other analysis shows the biggest losers between now and 2020 will be lower income families, with the poorest third likely to see incomes drop.
Chancellor Philip Hammond said millions of new jobs had been created.
Defending his Autumn Statement plans, the chancellor told Radio 4's Today programme that the government had brought job growth. It was investing for the future, preparing for a "rainy day", and government borrowing was on a "downward path", he added.
In its analysis of the Autumn Statement, the independent think tank, the IFS, said workers would earn less in real wages in 2021 than they did in 2008.
"This has, for sure, been the worst decade for living standards certainly since the last war and probably since the 1920s," said Paul Johnson, director of the IFS.
"We have seen no increase in average incomes so far and it does not look like we are going to get much of an increase over the next four or five years either."
The "outlook for living standards and for the public finances has deteriorated pretty sharply over the last nine months", he added.
Real average earnings - which factor in the rising cost of living - were forecast to rise by less than 5% between now and 2021. That forecast is 3.7% lower than was projected in March.
"Half of the wage growth projected for the next five years back in March is not now projected to happen. On these projections real wages will, remarkably, still be below their 2008 levels in 2021," Mr Johnson said.
"One cannot stress enough how dreadful that is - more than a decade without real earnings growth. We have certainly not seen a period remotely like it in the last 70 years."
The biggest impact on income in recent years, according to the IFS, has been felt by younger workers. Those aged 60 and over, in contrast, have seen living standards rise.
The squeeze on living standards could be worse during this Parliament than between 2010 and 2015, suggests the Resolution Foundation think tank. which campaigns for people on low and middle incomes.
Lower growth in pay, an accelerating rise in the cost of living, and welfare changes such as a freeze on working age benefits all combined to show that incomes on average would only grow by 0.2% a year, it said.
This compares to a rise of 0.5% during the coalition government years - a period of austerity in the aftermath of the financial crisis.
"Taking all this together we can look at the outlook for family incomes in the coming years, and it paints a grim picture," the think tank said.
Significantly, given the government's focus on "just about managing" families, the data shows that lower income families will be worse off.
The Foundation said the poorest 10% would see an income hit of more than 3% by 2020 as a result of tax and welfare policies.
"While top earners were hit the hardest following the financial crisis, the big difference looking forward is that the biggest losers are lower income families, with the entire bottom third of the income distribution set to see incomes fall in the years ahead," the Foundation said.
The Treasury's own analysis, published alongside the Autumn Statement, shows that the poorest 30% of households will see a negative impact on incomes from tax, welfare and public spending measures by 2019-20.
Primarily, this is a result of the main working age benefits and tax credits being frozen in cash terms for four years from April 2016. That includes entitlements such as jobseeker's allowance and income support.
That income freeze is forecast to coincide with an acceleration in inflation, pushing up the cost of living.
The chancellor offered some help to the lowest paid with changes to Universal Credit - the new umbrella benefit gradually being introduced across the UK.
Mr Hammond announced a reduction in the rate at which the benefit is withdrawn from people when they start work.
The Resolution Foundation report said this would have relatively little impact on family finances.
"When set against all other policy changes announced since the 2015 election, the Autumn Statement only undoes 7% of the hit from benefit cuts to the bottom half of the income distribution," it said.
Middle-income families will see some rises in income, but by no more than 1%, the Treasury documents show. The richest 10% will see the biggest hit to incomes.
More broadly, the IFS said that the OBR had forecast that national income in 2020-21 would be £30bn lower than projected in March - the equivalent to £1,000 per household.
Among Mr Hammond's announcements were:
The IFS said that Mr Hammond had clearly put whatever money he had into long-term plans.
"The clear prioritisation by Mr Hammond to direct most of what largesse he felt able to afford to paying for additional investment spending - roads, housing, research and development - to support the economy in the long run, rather than to pay to support the incomes of the "just-about-managing", or indeed public services, in the short run," Mr Johnson said.
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UK aviation regulator the CAA sought a joint no-deal transition plan with its EU counterpart but was rebuffed, correspondence seen by the BBC reveals.
The letters show the European Aviation Safety Agency (EASA) rejected a British call for a plan in July.
With months to go before the UK could drop out of the EU without a deal, the two bodies are yet to begin formal discussions.
EASA said technical talks could not pre-empt political agreement on Brexit.
In a letter to EASA in June, CAA chief executive Richard Moriarty said a "joint transition plan" was necessary to help assure people of "the on-going integrity of the aviation framework in any future scenario".
It said: "My team is standing by to support these discussions."
In response, EASA executive director Patrick Ky said he understood the request to limit disruption and safety risks.
But he added: "It remains the case that without sufficient clarity on both the outcome of the withdrawal process and the future UK legal framework such discussions would currently be premature."
If the UK leaves the EU without reaching a deal, the EU would not recognise certificates, approvals and licences issued by the CAA.
This could stop new aviation parts made in the UK - like wings constructed by Airbus - being put on EU planes.
British pilots with UK licences flying EU-registered aircraft would need to get second licences from another EU state or transfer their licences there.
The UK wants to participate in EASA after Brexit. Failing that, officials seek a deal where the EU and UK aviation authorities recognise each other's standards.
EASA has recently offered some UK aviation businesses the chance to be approved as "third county" suppliers to the EU, which means they could carry on doing business in the EU.
But not all areas of aviation are covered.
Although there are international agreements, there is no aviation equivalent of the World Trade Organization that would allow flights to continue seamlessly after a no-deal Brexit.
In a statement to BBC Radio 4's Today programme, EASA said Brexit negotiations were ongoing and added: "The outcome of those negotiations cannot be pre-empted, but until more clarity is gained of the terms of UK's withdrawal, discussion about technical details would not be useful since the framework for which we need to prepare is not known.
"Such technical-level discussions cannot pre-empt the overall political agreement, which is the subject of the withdrawal negotiations.
"Once the future framework is clearer, we will be open to engaging also in technical discussions."
The CAA said the UK would recognise safety licences and approvals issued by EASA and it urged EASA to recognise its own after Brexit.
A spokesman said: "We call upon the European Commission to allow EASA to hold discussions with us about the detailed technical arrangements that would apply in a no-deal scenario.
"We are ready to start these talks immediately."

A High Court ruling that Parliament - not the government alone - can trigger Article 50 threatens to delay Theresa May's timetable for leaving the EU, but could it spell the end for Brexit altogether?
Downing Street says it is confident that the Supreme Court will overrule the High Court and allow ministers, rather than MPs, to decide when to begin the formal process of leaving the EU.
But there is no evidence that government lawyers have yet amassed new arguments that might persuade the highest court in the land that the three eminent judges reached the wrong conclusion on Thursday.
So if that ruling stands, then the relevant secretary of state, David Davis - in charge of the process of exiting the EU -  has said his presumption is that an Act of Parliament would be required before triggering Article 50 of the Lisbon Treaty. No 10 has said that's the 'logical conclusion' of the ruling, too.
Incidentally a former Conservative leader - Iain Duncan Smith - disagrees, and believes a straightforward vote of MPs would satisfy the courts.
But let's assume government ministers are right.
Could the mere act of consulting largely pro-Remain MPs scupper Brexit?
Well, no.
Although the former chancellor Ken Clarke and the former Lib Dem leader Nick Clegg have told the BBC that they are prepared to vote against invoking Article 50, enough Remainers are saying they would respect the result of the referendum and vote to start the process of leaving the EU. The government would not lose this vote.
More likely is delay - rather than destruction - of Brexit.
But the opportunities for delay depend in part on the form any legislation would take.
Some pro-Brexit politicians are urging the government to come up with a simple one-line bill triggering Article 50.
The shorter and simpler the legislation, the more difficult it would be for Remainers to put forward elaborate amendments attempting to tie the government's hands in subsequent negotiations with the EU.
The former attorney general Dominic Grieve reckons that amendments could still be permitted, so long as they were addressed to the narrow substance of the bill.
This could allow, for example, an amendment to hold a second referendum on the final deal negotiated by the government, given that those negotiations were triggered by the Article 50 process - the option favoured by the former Labour leadership contender Owen Smith.
Even assuming that all amendments were defeated or ruled out of order, any legislation at all carries a risk for the government.
That's because it needs to be approved not just by the Commons but by the Lords.
And many pro-Remain unelected peers might be less squeamish than MPs about voting against Article 50.
If - and it's a big if - that were to happen, then the government would have to use the Parliament Acts to overrule them. Peers cannot stop legislation outright - they can simply force a rethink.
That would delay the process by about a year - scuppering not Brexit itself, but Theresa May's promise to start the process by the end of March 2017.
It might also extend our membership of the EU until just after the next general election, in the spring of 2020.
Some pro-Brexit Conservatives are already urging the prime minister to call an early election under these circumstances, on a platform of standing up for "the people" against "the peers".
With the party's lead in the polls, they calculate that this would strengthen the government's mandate.
But, given the complications and potential consequences of yesterday's ruling, you can understand why minsters are keeping their fingers firmly crossed that the Supreme Court will overturn it.

The EU must back Theresa May's Brexit plan or risk the UK leaving without a deal, the most senior member of the UK PM's cabinet has said.
Cabinet Office Minister David Lidington said the European Commission's proposals remained unacceptable.
And he appealed for compromise from the EU side in Brexit talks.
The EU's chief negotiator Michel Barnier said the EU was ready to offer the UK an unprecedented deal but it must not weaken the single market.
Speaking to a French business conference, Mr Lidington, who is Mrs May's de facto second-in-command, suggested there were only two choices on the table as Brexit talks entered a critical phase.
"With exactly seven months until the end of Article 50 process and less than two months ahead of the October European Council, we face the choice between the pragmatic proposals we are discussing now with the European Commission, or the risk of there being no deal.
"The alternative models do not meet the level of ambition or the outcome we all want to see delivered.
"So, we need the EU to engage with us on our positive vision of the future relationship."
His message was softened from a version of the speech released to journalists beforehand, which had simply warned of "no deal".
Mr Lidington was branded "arrogant" by the People's Vote campaign for another EU referendum, which added: "Good deal, bad deal or no deal, Brexit is a big deal and it must be for the people to decide."
It came as Brexit Secretary Dominic Raab denied reports Michel Barnier has turned down UK requests for extended meetings in Brussels.
Mr Raab was said by The Guardian to have been frustrated by the EU chief negotiator's alleged failure to make himself available for talks.
But Mr Raab told a Lords Committee he had a "good professional and personal rapport" with Mr Barnier.
And he would be holding a "long" meeting with him on Friday.
Mr Raab vowed to increase the pace and frequency of talks with Mr Barnier when he took over in July from David Davis, who quit as Brexit Secretary in protest at Theresa May's white paper on trade with the EU when Britain leaves.
"I'm confident that a deal is within our sights," Mr Raab told the Lords EU Committee. "We're bringing ambition, pragmatism, energy and if, and I expect it will be, and if it is matched, we get a deal."
He added: "Firstly, in relation to whatever tittle tattle may appear in whatever newspaper, I shall be over in Brussels tomorrow (Thursday) evening for a long, substantive meeting on Friday, I hope that gives you the facts directly with Michel Barnier."
Britain is on course to leave the EU on 29 March.
Both sides are hoping to agree a divorce deal and a statement on future trading relations by the next EU summit on 17 October - but Mr Raab suggested that deadline could slip, saying there was a "possibility that it may creep beyond" that date.
On the £39bn Brexit "divorce bill", Mr Raab said a no-deal scenario could affect arrangements over payments to the EU.
"I don't think it could be safely assumed on anyone's side that the financial settlement as has been agreed by the withdrawal agreement would then just be paid in precisely the same shape or speed or rate if there was no deal."
And he rejected claims by pro-EU Labour peer Lord Liddle that any deal document was likely to be "vacuous" and "opaque", saying he expected it to contain a "degree of detail" and some "clear choices".
Theresa May's chief Brexit advisor Olly Robbins will no longer have to face questions from MPs or peers, Mr Raab told the committee, which was holding a special meeting during Parliament's summer recess.
The two men were grilled by MPs in a joint appearance before the Commons Brexit committee in July.
But Mr Raab told the Lords EU committee that in future it would be ministers only - and not civil servants - that "come and be accountable" to Parliamentary committees over Brexit.
Meanwhile Mr Barnier, speaking Berlin, said the EU was "prepared to offer Britain a partnership such as there never has been with any other third country".
But, he added, it would not permit anything that weakened the single market.
"We respect Britain's red lines scrupulously. In return, they must respect what we are. Single market means single market ... There is no single market a la carte," he told reporters.
The pound rose 0.6%, to around $1.2950, after the EU chief negotiator's comments.

It's going to be quite a baptism of fire for the UK's new Brexit secretary on his first visit to Brussels in the new job.
He'll hardly have a foot through the door at the European Commission before he's faced with a barrage of questions. The EU wants clarity on the UK's negotiating position: is it based on Theresa May's Chequers cabinet agreement or the subsequent parliamentary amendments? Will the UK position change again in a few days or a week's time?
The EU's chief Brexit negotiator Michel Barnier then has another message he's hell-bent on delivering. Work with us, he will say to Dominic Raab, to finish the UK's exit deal - the so-called Withdrawal Agreement - otherwise the chances are rising of the UK crashing out of the EU without a deal come March next year.
Now coincidence of coincidences, just as Mr Raab arrives in town, the European Commission will publish a paper instructing EU governments to do more to prepare for the possibility of a no-deal Brexit which - it warns - would have a considerable impact on European businesses and citizens.
The paper mentions amongst other things the potential immediate impact on EU borders - with goods and people from the UK subject to customs checks. It predicts the aviation industry could be severely disrupted- with EU-UK airline and passenger rights agreements no longer valid. It advises that personal data transfers to the UK would be subject to new limitations and that the City of London would no longer have financial passporting rights.
The paper also alerts pharmaceutical companies to the fact that the testing of European medicines could no longer to be carried out in the UK in the case of a no-deal Brexit and it informs that the UK would have to be removed from EU databases.
Contrary to some UK media reports which suggest that the Commission's "preparedness paper" as it's known is being published now as a result of the political turmoil and uncertainty in Westminster, this is something the Commission has been working on for months. The Commission likes to say it began its preparedness research when the UK government began the mantra of "no deal is better than a bad deal" though that, I think, is questionable.
I've seen a draft of the preparedness paper but have been told it is a work in progress and will only be finalised on Thursday morning, just in time for Mr Raab's Brussels arrival.
As one senior EU diplomat put it to me: "When it comes to Brexit, there are no innocent timings."
Having had a lot of background chats with senior European officials of late, I can say with certainty that the Commission paper is not simply a scaremongering exercise.
There is genuine concern in Brussels that:
The EU thinks a Brexit no-deal scenario would be a bureaucratic, practical and financial nightmare for Europe.
So expect Mr Barnier to adopt encouraging tones with Mr Raab, reminding him that the Withdrawal Agreement is already 80% signed off between the EU and UK.
However, the 20% left is challenging to say the least - covering flashpoints like data protection, UK military bases in Cyprus and who should police the withdrawal agreement and subsequent almost two-year transition period.
On the Irish border backstop - where both the EU and UK have undertaken to avoid the re-introduction of a hard border between Northern Ireland and the Ireland whatever their post-Brexit relationship looks like - the Commission, I'm told, is working on rewording the protocol in the declared hope that will make it easier for team Theresa May to sign up to.
Former EU trade official Peter Guilford told me this week he believes the Brussels rumours that Brexit talks will go down to the wire this autumn and it would only be when the Commission "saw the whites of UK negotiators' eyes" that they would start making their own compromises instead of always hammering the UK for them.
But EU diplomats wonder: can Theresa May hang on till then?

The UK must come forward with proposals aimed at avoiding a hard border in Ireland, the EU's chief Brexit negotiator has said.
Michel Barnier said it is, so far, unclear what the UK is willing to commit to in Northern Ireland.
That echoes the position of the Irish government.
It wants the UK to give more commitments before the Brexit talks can begin considering a trade deal.
The prime minister has repeatedly said that the "unique circumstances" of Northern Ireland will require a "specific" solution.
During a speech in Brussels, Mr Barnier focused on the issue of what EU rules may continue to apply in Northern Ireland after Brexit.
He said: "There are over one hundred areas of cross-border co-operation on the island of Ireland.
"Such co-operation depends, in many cases, on the application of common rules and common regulatory space."
He added that the UK has said it would continue to apply some EU rules on its territory after Brexit but it is "unclear what rules will apply in Northern Ireland after Brexit".
UK ministers and unionist politicians have said they will not accept an arrangement which will "endanger the integrity of the UK single market".
However, Mr Barnier said Northern Ireland already has specific rules in some areas that are different to the rest of the UK.
He pointed to the "all-island" single electricity market, or specific regulations for plant health for the whole island of Ireland.
The DUP has criticised Mr Barnier's comments, describing them as an attempt to "bully the UK government toward support for a Brexit border scenario which would weaken Northern Ireland's constitutional position and devastate the local economy".
MEP Diane Dodds said any Brexit deal must reflect the fact that Great Britain is, by far, Northern Ireland's most important marketplace.
"We will not be cut off from the rest of UK either by associate membership of the EU or by regulatory divergence from Great Britain," she said.
"The DUP will exert our influence to ensure this is the case."
On Friday, Prime Minister Theresa May was told she had two weeks to makes progress on the border and the Brexit bill if the EU is to agree to begin Brexit trade talks before the end of the year.
EU Council President Donald Tusk said he was "ready" to move onto the next phase of Brexit talks, covering future relations with the UK.
But he said the UK must show much more progress on the "divorce bill" and the Irish border by early next month.
Mrs May said "good progress" was being made but more needed to be done.

There can be no Brexit withdrawal agreement without a "backstop" option for the Irish border, the EU's chief Brexit negotiator has said.
Michel Barnier said the Republic of Ireland has the full support of all EU member states and all EU institutions.
The backstop would involve NI, or the UK as a whole, aligning with the EU rules required to support North-South cooperation and an all-island economy.
Mr Barnier was speaking at the start of a two-day visit to Ireland.
The UK has accepted the need for a backstop to be written into the Brexit withdrawal agreement.
But it has not agreed what EU rules it should cover.
At the beginning of the all-island Brexit forum in Dundalk, County Louth, Mr Barnier said he knows that the so-called backstop has been the subject of "heated discussions in the UK".
"To be clear: without a backstop, there can be no withdrawal agreement," said Mr Barnier. "This is an EU issue, not only an Irish issue."
It almost became Brexit bingo - as journalists lost count of how many times Mr Barnier referenced the "backstop" option for the Irish border.
The backstop would mean that in the absence of any other solution, Northern Ireland, or the UK as a whole, would align with EU rules required to support north-south cooperation and an all-island economy.
While in principle the UK signed up to this option, precise detail on it has yet to appear.
Mr Barnier's three points were:
In brief - the backstop was agreed - so let's get on with it.
Mr Barnier also denied claims from Arlene Foster, the leader of the Democratic Unionist Party (DUP), that he has been "aggressive" towards Northern Ireland unionists in the Brexit talks.
The DUP leader said earlier that Mr Barnier did not understand the dispute and was not an "honest broker".
In response, the EU's chief Brexit negotiator said he was not ready to engage in "polemics" with Mrs Foster.
Mr Barnier's visit comes amid rising tensions over the future UK-Ireland border.
He told a press conference in Dundalk at the beginning of the all-island Brexit forum that his "door is open" to Mrs Foster and the DUP.
He said he had not approached the negotiations in a "spirit of revenge".
He added that he regretted the UK had voted to leave the EU, and said he was determined to work with the UK to find a solution to the Irish border issue.
The all-island Brexit forum is being hosted by the Taoiseach (Irish prime minister) Leo Varadkar and his deputy, Simon Coveney.
On Sunday, Mr Barnier said the UK was contradicting itself over its Irish border policy.
But Mrs Foster said she believes Mr Barnier does not understand the dispute and is "not an honest broker".
In return, he said that Mrs Foster needed to respect that his role was to negotiate on behalf of the EU and not to act as a mediator.
Meanwhile the Taoiseach again there needed to be "meaningful progress" on the border issue by the June EU summit.
Mr Varadkar said otherwise it would be difficult to get the withdrawal agreement in place by October.
In December, the UK and EU reached a political agreement in which the UK committed to protecting north-south cooperation on the island of Ireland.
It also guaranteed there would be no hard border, including physical infrastructure or related checks and controls.
However, the EU's proposed backstop solution to avoid a hard border - keeping Northern Ireland in the customs union after Brexit - continues to be at odds with what the UK government and the DUP say they would accept.
Mrs Foster told BBC political editor Laura Kuenssberg the DUP would not accept Northern Ireland being treated differently to the rest of the UK.
She said: "Michel Barnier's trying to present himself as someone who cares deeply about Northern Ireland and if that is the case he needs to hear the fact that we are part of the United Kingdom [and] will remain part of the United Kingdom constitutionally, politically and economically.
"Therefore his proposal of us being in an all-Ireland regulatory scenario with a border down the Irish Sea simply does not work.
"It does not work constitutionally, politically and it certainly does not work from an economic perspective."
Mrs Foster added: "We've tried to get him to understand the unionist position for the people of Northern Ireland but he hasn't really responded and I'm disappointed about that.
"I don't think he does understand the wider unionist culture of Northern Ireland."
The DUP is also expressing annoyance that Mr Varadkar is visiting Northern Ireland later without giving notice.
Mr Barnier is due to meet Mr Varadkar on Monday and will also speak to business leaders on both sides of the Irish border during his trip.

Michel Barnier has clarified remarks he is reported to have made about Brexit.
The EU negotiator was quoted as saying he saw the process as an opportunity to "teach" the British people and others what leaving the single market means.
Mr Barnier said he actually told a meeting it "was an occasion of great explanation for everyone in the EU".
The BBC understands he was talking in Italy about explaining the benefits of the single market to a broad European audience, not just specifically the UK.
The latest round of negotiations over the UK's exit from the EU concluded last week, with the two sides due to officially meet again later this month.
The UK, which is keen to move on from issues directly related to its withdrawal to talk about its future relationship with the EU, has said it would like to "intensify" the pace of talks, with Downing Street saying it is open to holding negotiations on a rolling basis.
There has been unconfirmed speculation that Prime Minister Theresa May is to make a major speech on Brexit later this month in the run-up to the Conservative Party conference.
Speaking at a conference in Italy on Saturday, Mr Barnier said he did not want to punish the UK for voting to leave the EU in last year's referendum.
But he reportedly warned that "there are extremely serious consequences of leaving the single market and it hasn't been explained to the British people".
"We intend to teach people… what leaving the single market means," he reportedly told the Ambrosetti forum.
Responding to the remarks, a No 10 spokesman said "the British people have heard those arguments."
Mr Barnier tweeted on Monday that what he had said was that Brexit was an "occasion to explain single market benefits in all countries, including my own".
He added "we do not want to "educate" or "teach lessons".
The former French minister, who met the Irish Republic's Foreign Minister Simon Coveney for talks on Monday, later reiterated these comments when speaking to a BBC reporter outside the European Parliament.
Amid growing tensions between the two sides about the progress of talks and the priority given to different issues, a senior EU official has said talks about the UK's financial obligations after Brexit are going backwards.
Gunther Oettinger, the European Commissioner responsible for the EU budget, said "the Brits have to accept that their obligations are going beyond March 2019".
"In July we had been thinking 'yes, they are on the way to accept it'. Now in the last few days they are coming back," he told a technology conference in Brussels.
BBC Brussels reporter Adam Fleming said Mr Oettinger had told him he believed that progress made on the issue in the July round of talks had been reversed during last week's session.
A source at the Department for Exiting the EU said it did not recognise this description and that there had been a robust debate about money.
Last week British officials gave a three-hour long presentation on the legal basis of the EU's request for a Brexit financial settlement.

The UK has until the end of 2020 to change its mind about leaving Europe's single market, the European Union's chief Brexit negotiator has said.
Michel Barnier said that if the UK changed its "red lines" during the post-Brexit transition period, the EU would also change its position.
Theresa May says the UK will quit the EU single market and customs union.
She says this is needed to ensure the UK has the power to control borders and do trade deals with other countries.
The UK is set to leave the EU in March 2019, at which point the transition phase - which the UK government calls the implementation phase - will begin. This will last until 31 December 2020, when the final arrangements agreed between the two sides will kick in.
Negotiations are under way between the two sides, but the UK has already said it plans to leave the single market, which provides for frictionless trade across borders and involves the free movement of people between member states.
In an interview with reporters from several European newspapers, Mr Barnier said the UK would not leave the single market and customs union until 31 December, and until this date, "everything is possible".
"If the UK wanted to change its red lines, we would therefore change ours," he said.
Mr Barnier added that he was not expecting this to happen, but that the EU would not be dogmatic.
He suggested the UK could follow a similar model to Norway, which has access to the single market in return for a financial contribution, accepting EU law and allowing the free movement of people.
This is one of those moments where Michel Barnier says things he has said before but in a way that is revealing about how the rest of the Brexit process will unfold.
The EU doesn't think the future relationship with the UK will be finalised by the date of its departure on 29 March 2019.
Which means that during the transition/implementation phase the UK could change its mind - quite significantly - about what it wants and then negotiate on that basis.
It also suggests that the EU wants the document sketching out the shape of the future relationship which will be agreed during the next phase of talks this year to be very, very open - not the detailed blueprint the British government seeks.
On the current trajectory, the UK will be out of the EU in 2019 but the arguments about whether it should remain in the customs union and the single market could carry on right up until a deal on the future relationship is sealed.
The UK government says it wants a comprehensive, bespoke free trade trade deal with the EU to replace its single market membership.
It wants to agree this by the Autumn in time for a "withdrawal agreement" to be ratified by the UK and EU Parliaments by March. But the EU has suggested only a "political declaration" will be possible by this deadline.
On Tuesday, the European Council's president said Brexit makes him "furious".
Speaking in Dublin, Donald Tusk said the UK's departure from the EU was "one of the saddest moments in twenty-first century European history".

They seek it here, they seek it there - but the centrepiece of the government's Brexit legislation, the EU (Withdrawal) Bill, seems to have gone into hiding.
Most Westminster observers expected the Commons to embark on eight days of detailed debate, in Committee of the Whole House, pretty much as soon as their conference recess was over.
Eyebrows were raised when it was not on this week's agenda - and they shot skywards when it was not put on the agenda for next week.
It is not a postponement, because the committee stage has never been scheduled, but something seems to be afoot.
What might it be? Challenged in Commons business questions by the SNP's Pete Wishart, Leader of the House Andrea Leadsom noted that MPs had proposed more than 300 amendments and 54 new clauses to the Bill and these were being studied by ministers.
And there is little doubt that some of these pose a real threat to the government's tenuous Commons majority.
The threat-in-chief is posed by amendments from the Conservative former attorney general, Dominic Grieve, to limit ministers' powers to re-write the law in the process of enacting Brexit.
Remember, this Bill is designed to allow the government to reprocess four decades of accumulated EU law into British law, so that the UK has functional legislation on all kinds of crucial areas, come Brexit Day.
The powers are pretty sweeping, because the Bill provides a toolkit to build an edifice which has not yet been designed - and Mr Grieve's amendments express the qualms of some MPs (including those of many strong Brexiteers) about their extent. He is the man most likely to amend.
I suspect the government is already whispering to him, behind the scenes, to produce an appropriate compromise, probably with the helpful endorsement of the Commons Procedure Select Committee behind it.
Was that the PM's bag-carrier, Seema Kennedy, I spotted in the public galler, when Mr Grieve set out his stall in evidence to the Procedure Committee on Wednesday?
If ministers can craft a compromise amendment, via ProcCom, face can be saved and division averted.
But with plenty more amendments still raining down, Mr Grieve is not the only threat. A recent addition is an amendment co-signed by the Nottinghamshire axis of Conservative ex-chancellor Ken Clarke and Labour's arch-Europhile, Chris Leslie.
This is a cunning production which takes the PM's commitment to a transition from full EU membership to Brexit, made in her Florence speech, and seeks to put it on the face of the Bill.
It follows her words precisely. But the killer point is that, if there's no transition, then a fresh act would be required to trigger Brexit day. In other words, if no transition, then they must come back and ask Parliament "what next?"
Now the government is not legislating against the clock as it was on the Article 50 Bill, when it was racing to get the measure through Commons and Lords before the end of the last Parliamentary year.
But its schedule is clearly slipping a little.
Next week is to be devoted to a little humdrum legislation, an opposition day debate and backbench business - that leaves seven debating weeks before Parliament embarks on its Christmas recess.
Take out one week to debate the Budget, and another for the November mini-half term (when a lot of select committee visits have been scheduled) and you have six weeks in which to cram the promised eight committee stage days devoted to the Bill, and the minimum of two days needed for report stage and third reading. Not impossible - but it does make for a packed Parliamentary programme, with little room for anything else.
There is rising speculation that the continuing delay in getting going reflects ministerial indecision about how to handle the amendments to the Bill - although another theory is that the government is waiting until next week's European summit is done, in the hope that it can firm up the terms of a possible transitional arrangement.
But the heat is on.

John Bercow has vowed "creativity" in Parliament if Boris Johnson ignores a law designed to stop a no-deal Brexit.
The Commons Speaker also said in a speech that the only possible Brexit was one backed by MPs.
A new law, passed before the suspension of Parliament, forces the PM to seek a delay until 31 January 2020, unless a deal or no-deal exit is approved by MPs by 19 October.
The PM has said he would rather be "dead in a ditch" than ask for a delay.
Responding to Mr Bercow's comments, Tory Brexiter MP Sir Bernard Jenkin said the role of the Speaker had become "irretrievably politicised and radicalised".
Meanwhile, Downing Street has announced Mr Johnson will travel to Luxembourg on Monday to hold talks with European Commission President Jean-Claude Juncker, and the country's prime minister Xavier Bettel.
Delivering a lecture in London, Mr Bercow said: "Not obeying the law must surely be a non-starter. Period."
He said it would be a "terrible example to set to the rest of society".
"The only form of Brexit which we will have, whenever that might be, will be a Brexit that the House of Commons has explicitly endorsed," he said.
"Surely, in 2019, in modern Britain, in a parliamentary democracy, we - parliamentarians, legislators - cannot in all conscience be conducting a debate as to whether adherence to the law is or isn't required."
He called it "astonishing" that "anyone has even entertained the notion".
If the government comes close to disobeying the law, Mr Bercow said that Parliament "would want to cut off such a possibility and do so forcefully".
"If that demands additional procedural creativity in order to come to pass, it is a racing certainty that this will happen, and that neither the limitations of the existing rule book nor the ticking of the clock will stop it doing so," he added.
The new law could force a Brexit delay beyond the current 31 October deadline by requiring the prime minister to request an extension to the UK's EU membership.
This would be done by making him write to EU leaders to prolong talks under Article 50 - the part of the EU's Lisbon Treaty which sets out what happens when a country decides that it wants to leave the EU.
The law forcing the PM to seek a delay unless MPs vote for a deal or no deal received royal assent on Monday, the final day that MPs sat in this session.
Parliament was suspended - or prorogued - in the early hours of Tuesday and is not scheduled to return until 14 October.
Foreign Secretary Dominic Raab has said the government would abide by the law, but would "test to the limit" what it requires of ministers.
Mr Bercow said: "One should no more refuse to request an extension of Article 50 because of what one might regard as the noble end of departing from the EU as soon as possible, than one could possibly excuse robbing a bank on the basis that the cash stolen would be donated to a charitable cause immediately afterwards."
Sir Bernard, who chairs the constitutional affairs select committee in Parliament, said the Commons should "adapt itself" to a new role for the Speaker.
He accused Mr Bercow of launching a "personal attack" on the prime minister, insisting this would have been "unthinkable 10 or 15 years ago".
The current position allows the occupant "unregulated and untrammelled power", he told BBC Radio 4's Today programme.
"It's a kind of majoritarian dictatorship position," he added.
Another Leave-voting Conservative MP, Michael Fabricant, said Mr Bercow had brought the office of Speaker into disrepute:
However, shadow chancellor John McDonnell said Mr Bercow was simply "exercising his proper role, which is to protect the right of Parliament".
He said a "sizeable number" of MPs across all political parties were against allowing the PM to "push us into a no-deal Brexit".
Such an outcome would be "against the will of Parliament, and I actually think against the will of the people as well," he added.
On Thursday, Mr Johnson insisted the UK "will be ready" to leave the EU by the current deadline without an agreement "if we have to".
In response to the publication of the government's Yellowhammer document, an assessment of a reasonable worst-case scenario in the event of a no-deal Brexit, Mr Johnson reiterated it was "the worst-case scenario".
"In reality we will certainly be ready for a no-deal Brexit if we have to do it and I stress again that's not where we intend to end up," Mr Johnson said.
Mr Bercow has announced he will stand down as Commons Speaker and MP at the next election or on 31 October, whichever comes first.
The House of Commons has confirmed an election to choose his successor will take place on Monday 4 November.
The Speaker's warning came as the EU's chief Brexit negotiator told political leaders in the European Parliament on Thursday that he could not say whether contacts with the UK government would result in a deal by mid-October.
Michel Barnier, in a speech to MEPs, suggested that negotiating a new withdrawal agreement remained uncertain despite discussions between Mr Johnson's team and the EU.
"I cannot tell you objectively whether contacts with the government of Mr Johnson will be able to reach an agreement by mid-October," he said.
"While we have previously reached an agreement, as far as we can speak, we have no reason to be optimistic."
He added: "We will see in the coming weeks if the British are able to make concrete proposals in writing that are legally operational."

The chancellor confirmed to MPs what has been widely known in Westminster for a long time.
Regular readers will know that from time to time I have ranted on about it here.
But Philip Hammond told MPs on Wednesday afternoon that indeed, it is the case that the cabinet has not yet had its big bonanza conversation about the "end state", when the prime minister will have to put her cards on the table finally, and explain the kind of relationship she wants with the EU after we leave, and after the transition period.
She will then have to try to persuade her cabinet colleagues to back her view.
It is a conversation that she has delayed for months, holding it back because she knows the cabinet is divided, and bringing them together could be extremely hard.
It boils down to this. Ministers like Boris Johnson and Michael Gove believe that Britain's future lies in striking out on our own, out of reach of most of the tentacles of the EU's institutions.
It is an over-simplification, but to explain the difference, you can point to the deal that Canada did with the EU, a free trade agreement essentially, where there is co-operation and collaboration to make it easy for business.
But there is nothing like the current situation - whether that's on immigration, rules for industry or the legal system. There is a strong and significant faction inside the Tory party that agrees with them and are extremely well organised and willing to make trouble if they see that possibility being undermined.
That's what explains the co-ordinated cage-rattling by Brexiteers since the first phase deal fell apart on Monday afternoon.
But there are others in Theresa May's team who think the best thing for business, and the best thing for the country is to mirror the EU's arrangements as far as we possibly can. The idea is that even though we will have left the EU, we preserve as much of our trading relationship as possible, even if that means continuing to be bound by many of the EU's rules and routines in all but name.
Again, it's a generalisation, but a relationship like Norway and the EU where they have very close ties (but not much influence) gives you a rough idea. Theresa May always says that she wants a "bespoke deal", but you can get a sense of the two different kinds of options here.
The technical term in Whitehall for the competing visions is "high or low alignment".
While the government disputes that it is only a choice of one or the other, politically in the Tory party it is a question of two "sides". And so far, the prime minister has avoided coming down completely on one side or another. Talk to ministers on different sides privately and they both seem to think Theresa May agrees with them, although they can't be completely sure..
There are intensely strong feelings in both camps, and so far, Theresa May's way of broadly avoiding arguments has been not to have the discussion.
Essentially what could be an enormous row, that might even end up with some members of the Cabinet resigning, has been postponed, rather than resolved.
But the crisis over the DUP has tightened the valve on what's a political pressure cooker. Because, to use the jargon, that dispute is essentially about 'alignment'.
The problem of Northern Ireland is the DUP's deep discomfort that Northern Ireland could be more closely aligned to the rest of the EU, and Dublin, than the rest of the UK. Basically, they don't want to be pulled more tightly to Dublin than to Westminster. It is its own deeply important, and sensitive, issue.
But it has forced the question of alignment more generally out into the open. And it's the first time the truce on the issue has been tested. How closely 'aligned' should  the UK really be outside the EU?
The prime minister had to make a call over the weekend to get to a potential deal to move on to the next phase of the Brexit talks.
But the way that deal held out the possibility of "high alignment", was simply not acceptable to many people in her party, as well as the DUP.
So now, the time is coming, and coming soon, when she will have to answer the question she's avoided answering in detail for many months. And the discussion she has been postponing in Cabinet for over a year.
There's a good reason. It's been to keep a lid on the ideological disputes that she knows exists.
On Wednesday afternoon Number 10 confirmed officially that the cabinet would have the discussion before Christmas. Her allies point again and again to the clues that she has given in her big interventions in the debate - whether the Lancaster House speech or her address in Florence.
On the question of alignment, sources in the Department for Exiting the European Union say that she made her position plain with this simple passage.
"There will be areas which do affect our economic relations where we and our European friends may have different goals; or where we share the same goals but want to achieve them through different means.
"And there will be areas where we want to achieve the same goals in the same ways, because it makes sense for our economies."
But the carefully constructed phrases she has put forward in her major speeches about Brexit have been, in a sense, sophisticated sticking plasters.
They have set out generalities, not specifics, and whether the implications were misunderstood or just ignored at the time, the reality of having to make actual decisions as the negotiations progress mean that sooner or later, she will have to rip them off.

Commons authorities have cast doubt on the idea that public donations could pay for the cost of making Big Ben chime when the UK leaves the EU.
Big Ben has been largely silent since refurbishment of its tower began.
But Boris Johnson has suggested crowdfunding could cover the costs of getting the bell working on 31 January.
The House of Commons Commission has said the estimated cost of up to £500,000 cannot be justified and using donations would be "unprecedented".
An amendment to the PM's Brexit bill, which would have required it to chime on Brexit day at 23:00 GMT, failed last week.
But on Tuesday, Mr Johnson told BBC Breakfast: "We're working up a plan so people can bung a bob for a Big Ben bong, because there are some people who want to."
The commission said ongoing work to the Palace of Westminster's Elizabeth Tower meant getting the chimes working again now would cost between £350,000 and £500,000.
The body - a group of MPs and officials responsible for the day-to-day running of Parliament - later issued a second statement raising concerns about any type of crowdfunding.
Any fundraising would have to be "consistent with principles of propriety and proper oversight of public expenditure", it said.
It added that the Commons had a "well-established" process by which it approved spending which allowed it to "preserve its constitutional position in relation to government".
When the restoration work started in 2017, it was agreed that Big Ben should sound for Remembrance Sunday, Armistice Day and New Year's Eve.
According to the commission, this arrangement was made so the project team could plan its works around the dates well in advance.
The House of Commons Commission's estimate for the cost of sounding Big Ben on Brexit day is made up of two separate parts:
The commission says the floor in the belfry has been removed and there would be a significant cost to put in and then remove a temporary floor.
As well as the floor, the £120,000 figure also includes the cost of installing and dismantling the temporary mechanism (an electric bell hammer) to sound the bell.
Commons Speaker Sir Lindsay Hoyle said: "The Commission believes it is important to weigh up the costs this would involve if Big Ben is to chime on 31 January.
"You are talking about £50,000 a bong. We also have to bear in mind that the only people who will hear it will be those who live near or are visiting Westminster."
However, Brexit Party leader Nigel Farage questioned the £500,000 figure, and accused the commission of "obstruction".
In an article for the Telegraph, he wrote: "It tolled on New Year's Eve, on Remembrance Sunday and on Armistice Day.
"Did this cost £500,000 on each occasion? I would love to know the answer."
Brexiteer Mark Francois, one of the Tory MPs behind the failed amendment, has said it would be "inconceivable" if Big Ben did not sound to mark the occasion.
But Labour MP David Lammy said £500,000 was a "huge amount of money to waste on jingoism".
The PM's official spokesman said there was not a "specific government fund" to meet the costs of getting Big Ben to chime on Brexit day.
But he added: "If the public wants Big Ben to bong and the money is raised, then that is great.
"We will make sure that - whatever happens in regard to Big Ben's bongs - January 31 is properly marked."

Incoming UK PM Boris Johnson faces "challenging" times, the EU has warned, as it reacted to his election as new Conservative leader.
Mr Johnson has the immediate task of guiding the UK out of the EU ahead of a 31 October deadline.
He says he wants to renegotiate an agreement with the EU, ditching large parts of the deal outgoing PM Theresa May struck last year.
But EU leaders have said the withdrawal agreement is not up for renegotiation.
The European Commission's newly elected President, Ursula von der Leyen, has however said she is willing to grant the UK another extension to Brexit talks, if London comes up with good reasons.
Congratulating Mr Johnson, Mrs von der Leyen said: "There are many different and difficult topics to tackle together. There are challenging times ahead of us. I think it is very important to build up a strong and a good working relation because we have the duty to deliver something that is good for people in Europe and in the United Kingdom."
The EU's Brexit negotiator, Michel Barnier, is due to meet MEPs on the European Parliament's Brexit Steering Group in an extraordinary meeting on Wednesday to respond to Mr Johnson's election.
US President Donald Trump meanwhile congratulated Mr Johnson on his victory, tweeting:
Later, he said: "We have a really good man is going to be the prime minister of the UK now, Boris Johnson. A good man. He's tough and he's smart. They're saying 'Britain Trump'. They call him 'Britain Trump' and people are saying that's a good thing. They like me over there.
"That's what they wanted. That's what they need... He'll get it done. Boris is good. He's going to do a good job."
In the often divisive Brexit world of "them and us", it is easy to forget that, beyond Brexit, EU leaders still see the UK as a close partner and ally.
Tuesday's messages of congratulation to Boris Johnson from across Europe were a timely reminder.
Whatever happens with Brexit, France, Germany, Poland et al still very much hope to work closely with the UK on international issues like Russia sanctions, Iran and human rights protection.
But EU leaders' welcoming tone does not signal a willingness to accept whatever Prime Minister Johnson might demand in terms of changes to the Brexit deal.
He's right when he says a no-deal Brexit is bad for Brussels, but he overestimates EU wiggle room. Amendments will only be forthcoming if EU leaders deem them workable and are convinced the new prime minister commands a majority in parliament to get the Brexit deal through once and for all.
In Germany, Chancellor Angela Merkel congratulated Mr Johnson, saying she would keep pursuing a "strong friendship" with London.
"I congratulate Boris Johnson and look forward to good co-operation. Our countries should continue to share a strong friendship in the future."
In a statement, her CDU party said they expect Mr Johnson "to pursue a responsible policy in Britain's interest. Responsible means - even for a Brexit hardliner - to prevent an unregulated Brexit at all costs".
German industry chiefs have also warned of the dangers of no-deal Brexit. Joachim Lang, CEO of the Association of German Industry, said: "Threats from London to leave the EU with no deal are harmful and will come back like a boomerang. They exacerbate damages that have already affected the economy."
Mr Johnson has pledged the UK will leave the EU on 31 October "do or die", accepting that a no-deal exit will happen if a new agreement cannot be reached by then.
France's President Emmanuel Macron praised outgoing Prime Minister Theresa May's "courage and dignity" and the fact that she had never "blocked the workings of the European Union".
On the new man in charge, he said: "I am looking forward to working with him, not only on European topics and the ongoing Brexit negotiations, but also on important international topics... such as Iran and international security."
Italy's Interior Minister and leader of the Lega (League) party, Matteo Salvini, tweeted: "Good job #BorisJohnson. The fact that on the left they depict him as 'more dangerous than the Lega' makes me like even him more."
The EU's chief Brexit negotiator Michel Barnier tweeted:
The deputy prime minister and foreign minister of Ireland, Simon Coveney, tweeted:

Boris Johnson has said he "won't be deterred by anybody" from leaving the EU on 31 October.
The prime minister said he was "cautiously optimistic" of getting a Brexit deal, but the UK would leave by the deadline "whatever happens".
EU chief Brexit negotiator Michel Barnier said he did not have "reasons to be optimistic" over getting a deal.
Mr Johnson will meet him and European Commission President Jean-Claude Juncker on Monday for talks.
During the PM's speech, at the Convention of the North in Rotherham, South Yorkshire, he was heckled by an audience member who told him to "get back to Parliament" and "sort out the mess that you have created".
Earlier this week Parliament passed a law forcing Mr Johnson to ask for an extension to Brexit.
He will have to write to the EU on 19 October to ask for an extra three months, unless he returns with a deal - then approved by MPs - or gets the Commons to back a no-deal Brexit.
But despite the new law, Mr Johnson said he would rather be "dead in a ditch" than ask for an extension.
The Speaker of the Commons, John Bercow, vowed to act with "creativity" if Mr Johnson ignored the law, saying it would be a "terrible example to set to the rest of society".
MPs managed to pass the law before Parliament was suspended - or prorogued - in the early hours of Tuesday morning until 14 October.
Mr Johnson said the government had made the move so it could hold a Queen's Speech and put forward its new domestic policy agenda.
But opposition MPs claim it was to stop scrutiny in Parliament of his Brexit plans.
Earlier this week, a Scottish court ruled the prorogation was unlawful as it was motivated by an "improper purpose of stymieing Parliament".
The government is appealing against the decision and a ruling will be made by the Supreme Court in London on Tuesday.
Answering questions after his speech, Mr Johnson said: "We are working incredibly hard to get a deal. There is the rough shape of the deal to be done.
"I have been to talk to various other EU leaders, particularly in Germany, in France and in Ireland, where we made a good deal of progress.
"I'm seeing [Mr Juncker and Mr Barnier] on Monday and we will talk about the ideas that we've been working on and we will see where we get."
He added: "I would say I'm cautiously optimistic."
MPs are still demanding Parliament be recalled to scrutinise a number of Brexit-related issues, including the release of so-called "Yellowhammer" papers - a government assessment of a reasonable worst-case scenario in the event of the UK leaving the EU without a deal.
But Mr Johnson said that "whatever the shenanigans that may be going on at Westminster", the government would "get on with delivering our agenda and preparing to take this country out of the EU on 31 October".
He added that there would still be "ample time" for MPs to scrutinise any deal reached with the EU, adding that he "very much hoped" to agree one at the EU summit on 17 and 18 October.
The Times newspaper reported that a Brexit deal could be on the horizon as the Northern Irish Democratic Unionists (DUP) - the party which has a confidence and supply deal with the Conservatives - had reportedly agreed to "shift its red lines" over the backstop.
The backstop is the policy in the existing withdrawal agreement - negotiated between former Prime Minister Theresa May and the EU - aimed at preventing a hard border returning to the island of Ireland, but it has proved controversial with a number of pro-Brexit MPs.
However, the reports were rejected by the DUP's leader Arlene Foster, who tweeted: "Anonymous sources lead to nonsense stories."
A UK spokesman in Brussels revealed the negotiating team had "presented some ideas" on an all-island Sanitary and Phyto-Sanitary solution - essentially keeping Northern Ireland aligned with EU regulations on animal and food health.
But the DUP has said it would not support any arrangement that could see Northern Ireland treated differently than the rest of the UK after Brexit.

Downing Street has hit back at Boris Johnson over his criticism of Theresa May's approach to Brexit, saying she is providing "serious leadership" and "a serious plan".
Mr Johnson has written in the Daily Telegraph that the approach agreed at Chequers "means disaster" for Britain.
The ex-foreign secretary said the PM's plan would hand the EU "victory".
But Mrs May's official spokesman said: "There's no new ideas in this article to respond to."
Downing Street said the prime minister's blueprint for future relations with the EU, hammered out with cabinet members at her country residence in July, was deliverable and could win the support of the House of Commons.
And former home secretary Amber Rudd told the BBC's Politics Live: "Once again, it's a case of leap before you look - there's absolutely no proposal here."
Ms Rudd said the Chequers plan represented "the best shot we have of Brexit that's going to work for the UK".
Mr Johnson resigned from the government in July in protest at the deal agreed by the cabinet at Chequers, the prime minister's country residence, as the UK's preferred way forward in negotiations with Brussels.
Other Tory MPs have also criticised the package, and the EU's chief negotiator, Michel Barnier, says he is "strongly opposed" to the proposals.
Mrs May's plan would see the UK agreeing a "common rulebook" with the EU for trading in goods, in an attempt to maintain frictionless trade at the border.
Critics argue this would leave the UK tied to EU rules after it leaves on 29 March 2019, and prevent Britain from striking its own trade deals in years to come.
If the UK and the EU do reach a deal, MPs will then have to approve it.
In his first intervention on the EU debate since quitting the government, Mr Johnson compared negotiations between Brexit Secretary Dominic Raab and Mr Barnier to a wrestling match.
He wrote: "The whole thing is about as pre-ordained as a bout between Giant Haystacks and Big Daddy; and in this case, I am afraid, the inevitable outcome is a victory for the EU, with the UK lying flat on the canvas and 12 stars circling symbolically over our semi-conscious head."
Mr Johnson said negotiations based on the Chequers plan had so far seen the EU take "every important trick", adding: "The UK has agreed to hand over £40bn of taxpayers' money for two-thirds of diddly squat."
He said by using the strategy - defended by Mrs May in the Sunday Telegraph over the weekend - the UK had "gone into battle with the white flag fluttering over our leading tank".
If it continued on the same path, Mr Johnson added, the government would "throw away most of the advantages of Brexit".
Mr Johnson also accused some members of the government of using the issue of the border between Ireland and Northern Ireland to "stop a proper Brexit", but added: "They have been rumbled."
The "scandal" around the border problem was "not that we have failed, but that we have not even tried", he added.
Mr Johnson argued that a hard border would not be needed after Brexit - because people did not need to be checked due to the Common Travel Area and that any checks on goods could be done away from the border.
In response, Mrs May's official spokesman said: "What we need at this time is serious leadership with a serious plan and that's exactly what the country has with this prime minister and this Brexit plan.
"She is a serious prime minister and she has put forward serious proposals."
But Tory Brexiteer Jacob Rees-Mogg, one of a group of MPs to meet Mr Barnier on Monday, suggested the EU negotiator agreed with him that the Chequers plan was "absolute rubbish" and he preferred the option of a looser arrangement based on Canada's trade agreement with the EU.
"Interestingly, Eurosceptics and Mr Barnier are in greater agreement than Eurosceptics and the government and between Mr Barnier and the government," Mr Rees-Mogg said. "It's very encouraging."
Labour's shadow foreign secretary Emily Thornberry told Politics Live that if Mrs May gave in Brexiteers, "she's going to end up coming back to Parliament with something that's not acceptable to Parliament... so then what happens?"
She added: "To hear some members of the Conservative Party play fast and loose with the [Northern Ireland] peace settlement is disgusting."
Scotland's First Minister Nicola Sturgeon described Mr Johnson as a "charlatan" who must share in responsibility for the "disaster" of Brexit.
Downing Street also rejected a proposal from former Conservative minister Nick Boles for the UK to stay in the European Economic Area to allow time for a new trade deal to be negotiated.
Mr Boles said the PM's plan, as it stands, has "close to zero" chance of winning support from Parliament while former education secretary Justine Greening told Radio 4's World at One that it was "more unpopular with the British public than the poll tax" and Theresa May should consign it to history.
"She should now accept it has not worked and look for alternative routes through," she said.
On Sunday, the prime minister wrote that she was "confident" a "good deal" could be reached on Brexit.
But she said it was right for the government to prepare for a no-deal scenario - even though this would create "real challenges for both the UK and the EU" in some sectors.

Tory leadership rivals Boris Johnson and Jeremy Hunt are at loggerheads over how the UK should leave the EU.
Both contenders for prime minister claim they can renegotiate a Brexit deal that the EU says is closed.
Mr Johnson said the UK must leave on 31 October "deal or no deal" but Mr Hunt called this a "fake deadline" that could trigger a general election if Parliament rejects a no-deal Brexit.
The winner of the contest will take over from Theresa May on 24 July.
The two men will face more questions from the public on Wednesday in a digital hustings, streamed on the Conservative Party's Facebook and Twitter accounts.
In an interview with Talk Radio, Mr Johnson insisted he would take the UK out of the EU by Halloween "come what may, do or die" and has challenged his opponent to make the same commitment.
Mr Hunt said he was prepared to leave without a deal, but not if there was a "prospect of a better deal".
During a phone-in on BBC Radio 2's Jeremy Vine Show, the Mr Hunt agreed with a caller who said the EU was "treating us like dirt", adding: "I don't think they've shown respect for us at all."
He has secured the backing of Scottish Conservative leader Ruth Davidson - who supported Sajid Javid and then Michael Gove in previous rounds - because she said he had "put the Union first".
A no-deal exit would see the UK leave the customs union and single market overnight and start trading with the EU on World Trade Organisation rules.
Opponents say it would cause huge disruption at the borders and be catastrophic to many firms reliant on trade with the continent - supporters say any negative effects would be manageable.
The EU has repeatedly insisted it will not re-open negotiations on the withdrawal agreement drawn up between Brussels and Theresa May - rejected three times by MPs.
On Wednesday, a European Commission spokeswoman confirmed that remained the bloc's position even if the only alternative was a no-deal exit.
Earlier, former Brexit secretary Dominic Raab, who is backing Mr Johnson, said Mr Hunt had shown "weakness" and "naivety" by entertaining the possibility of another extension.
He told BBC Radio 4's Today programme it would be the "EU's choice" to see the UK leave without an agreement, adding: "There is nothing stopping us getting a deal by October, if there's the political will."
He predicted "vanishingly few" Tory MPs would vote to bring down a government pursuing a no-deal exit in a vote of no confidence - even though Defence Minister Tobias Ellwood has said "a dozen or so" Conservatives could support such a move.
It comes as International Trade Secretary Liam Fox - who is backing Mr Hunt - again criticised Mr Johnson's claim that the UK could continue tariff-free trade with the EU in the event of a no-deal Brexit.
Mr Johnson has argued that a provision under the General Agreement on Tariffs and Trade - known as GATT 24 - could be used to avoid tariffs for up to 10 years.
But Mr Fox said this would require the agreement of the EU, which Brussels has made clear it would not give.
On Tuesday, Mr Johnson conceded that his plan would require the approval of the rest of the EU, but insisted it was still "an option".
Boris Johnson and Jeremy Hunt say they are serious about pushing for a no-deal Brexit if they are unable to negotiate a better withdrawal agreement with Brussels.
Yet the EU seems unfazed. Why, when we know EU leaders want to avoid a no-deal Brexit?
Part of the reason, at least, is time.
It's summer. European capitals are sweltering under a heatwave with government ministers counting the days until they hit the beach or find some cool mountain air.
The day the Brexit extension runs out - 31 October - seems an eternity away in political terms.
Also, just as Messrs Johnson and Hunt do not accept the EU's word when it says the Withdrawal Agreement cannot and will not be re-negotiated, EU leaders do not take them at their word when they threaten no deal by the end of October.
Former leadership candidate Rory Stewart, who is backing Mr Hunt, said the problem with Mr Johnson's plan was that he was just telling people "what they want to hear".
The international development secretary told the Today programme Mr Johnson was "pretending he has a magic solution" which was "not going to damage them at all", but the reality was he was going to let people down.
He also said he would definitely vote against a Tory government to stop a no-deal Brexit, but would stop short of backing a no confidence vote.
Mr Johnson continues to face scrutiny about Friday's row with his girlfriend Carrie Symonds, which prompted neighbours to call the police.
After days of criticism that he was hiding away, Mr Johnson undertook a series of media and public appearances on Tuesday - but declined to answer questions about the argument.
On Tuesday Mr Hunt told the BBC the next prime minister should be someone who is "trustworthy" and the ability to negotiate a new Brexit deal was about "personality", but stopped short of directly criticising his rival.
The day before, Mr Johnson told the BBC anyone questioning his character was "talking absolute nonsense".

Boris Johnson has criticised the UK government's Brexit talks strategy, saying it lacks "guts" and suggested Donald Trump could do a better job.
The foreign secretary also took a swipe at Chancellor Philip Hammond, calling the Treasury "the heart of Remain", in comments to a private dinner.
He said the Brexit talks were heading for "meltdown" and Leave supporters may not get the deal they expected.
Theresa May said Mr Johnson "had strong views on Brexit but so do I".
Speaking in Canada, where she is attending the G7 summit, the prime minister refused to be drawn on whether the foreign secretary was undermining her, a day after a row with her Brexit Secretary David Davis.
She said the process of leaving the EU was "complex" but her focus was on getting the right deal for Britain and people should judge her on her record in the negotiations so far.
In a recording, obtained by Buzzfeed, Mr Johnson warns the UK could remain "locked in orbit around the EU" and claimed the Irish border issue - one of the main sticking points in talks with Brussels - had been allowed to dictate "the whole of our agenda".
"It's so small and there are so few firms that actually use that border regularly, it's just beyond belief that we're allowing the tail to wag the dog in this way," he said.
The foreign secretary was apparently speaking to around 20 people in a private room after an Institute of Directors reception on Wednesday night.
It follows a day of wrangling over the government's "backstop" plan in the event of no customs deal being agreed before Brexit.
Theresa May was forced to agree to a cut-off date of December 2021 for any interim arrangements after Brexit Secretary David Davis threatened to resign.
But speaking to reporters on route to the G7 summit in Canada, she twice refused to give a "cast-iron guarantee" that the end date would not slip beyond that.
And speaking in Brussels, the EU's chief negotiator Michel Barnier said the proposal could only apply to Northern Ireland, not the UK as a whole, and questioned whether temporary arrangements were acceptable, telling journalists "backstop means backstop".
In the leaked comments, Mr Johnson said the prime minister was "going to go into a phase where we are much more combative with Brussels".
He added: "You've got to face the fact there may now be a meltdown. OK? I don't want anybody to panic during the meltdown. No panic. Pro bono publico, no bloody panic. It's going to be all right in the end."
Brexit will be "irreversible" and will happen, Mr Johnson said, but the "risk is that it will not be the one we want".
He added: "Unless you make the change, unless you have the guts to go for the independent policy, you're never going to get the economic benefits of Brexit. You'll never get the political benefits of Brexit."
He was said to have described concerns over the border between Northern Ireland and the Irish Republic as "pure millennium bug stuff" and suggested Chancellor Philip Hammond's department was "basically the heart of Remain".
Speaking about the Treasury, he added: "They don't want any disruption of the economy. So they're sacrificing all the medium and long-term gains out of fear of short-term disruption."
In response, Mr Hammond said his "advice to colleagues" was to engage with the EU as his experience was "a collaborative approach is generally more productive than a confrontational approach".
But Brexit-supporting MPs backed Mr Johnson, Peter Bone saying Mrs May "probably agrees with him as well".
The talks, he said, were "being held back by Remain officials who are driving this thing" - suggesting they should all be removed and Brexit Secretary David Davis given a "free hand".
No 10 said there was "rigorous debate" about Brexit but its focus was on delivering the deal the public wanted.
Scotland's First Minister Nicola Sturgeon said Mr Johnson was "simply not fit for the high office he holds" while Irish leader Leo Varadkar said "when I want to know what the view of the British government is, I listen to the prime minister".
Labour MP Rupa Huq, who campaigns against a "hard" Brexit, said Mr Johnson had been "very dismissive" of the risks to Northern Ireland, treating it - in her words - as a "small country that nobody bothers about".
Mr Johnson was the keynote speaker at Conservative Way Forward's summer reception and took questions for more than an hour, according to Buzzfeed.
Asked about Donald Trump, he reportedly said he was "increasingly admiring" of the US President and was "more and more convinced that there is method in his madness".
"Imagine Trump doing Brexit," he added.
"He'd go in bloody hard... There'd be all sorts of breakdowns, all sorts of chaos. Everyone would think he'd gone mad. But actually you might get somewhere. It's a very, very good thought."

Boris Johnson has refused to deny claims he used an expletive when asked about business concerns about Brexit.
The foreign secretary is reported to have used the swear word at a diplomatic gathering last week.
Asked about this in the Commons, he said he may have "expressed scepticism about some of the views of those who profess to speak up for business".
Theresa May said it was right the government listened to business voices about the terms of the UK's exit.
This story contains language some may find offensive.
Airbus, BMW and Siemens have warned about the impact on their UK-based operations if the UK leaves the EU next March without any agreement.
Their warnings have prompted different responses from ministers.
Business Secretary Greg Clark has said the UK must "take and act on the advice of business" but Health Secretary Jeremy Hunt said a warning from Airbus that it could cease operations entirely in the UK, threatening thousands of jobs, was "completely inappropriate".
Asked about corporate concerns over a so-called hard Brexit, at an event for EU diplomats in London last week, Mr Johnson is reported to have replied: "Fuck business."
Mr Johnson, who was reportedly speaking at the time to Rudolf Huygelen, Belgium's ambassador to the EU, was also overheard saying he and others would fight Theresa May's soft Brexit "and win".
The foreign secretary, who was a key figure in the Leave campaign, was pressed on the issue in Parliament by Labour MP Owen Smith, who asked him if the comments were correct and, if so, whether they could be "remotely justified".
"I don't think anybody could doubt the passionate support of this government for business," Mr Johnson said.
"It may be that I have, from time to time, expressed scepticism about some of the views of those who profess to speak up for business."
Mr Johnson's comments about Brexit have frequently proved controversial. He was recorded telling Tory donors last month that the UK's strategy lacked "guts" and suggested US President Donald Trump could do a better job.
The latest remark has angered some Tory MPs, with former Science Minister George Freeman telling BBC Radio 4's World at One programme that the reported comments were not "helpful, responsible or statesmanlike".
The prime minister, who will travel to Brussels on Thursday for a summit of EU leaders, told a chief executives summit hosted by the Times she wanted business to be able to speak to the government.
"It's right that we listen to the voice of business," she said.
"Business is at the heart of how we are going to develop this country," she said. "We want to ensure we are listening to the business voice because business provides the backbone of our economy."
MPs who favour a clean break with the EU after Brexit, in March 29 2019, have called on Mrs May to walk away from negotiations if the EU does not show willingness to begin trade talks immediately.

Boris Johnson has admitted he would need EU co-operation to avoid a hard Irish border or the possibility of crippling tariffs on trade in the event of a no-deal Brexit.
In an exclusive interview with the BBC, the favourite to be the next PM said: "It's not just up to us."
But he said he did "not believe for a moment" the UK would leave without a deal, although he was willing to do so.
Asked about a row he'd had with his partner, he said it was "simply unfair" to involve "loved ones" in the debate.
Reports of the argument on Friday with his girlfriend, Carrie Symonds, dominated headlines over the weekend after the police were called to their address in London.
The interview comes after Sky News said it would have to cancel a head-to-head debate on Tuesday between the two leadership contenders as Mr Johnson had "so far declined" to take part.
Work and Pensions Secretary Amber Rudd told Radio 4's Today programme she found Mr Johnson's decision to ignore live TV debates "very odd" and urged him "to reconsider".
Following days of criticism that he has been avoiding media scrutiny, Mr Johnson has given a number of other interviews, including with LBC and Talk Radio.
On LBC, he was repeatedly challenged on his personal life and a photograph which showed him and his partner. Asked whether his campaign was behind the release of the picture, Mr Johnson refused to answer.
He told Talk Radio's political editor Ross Kempsell he would "not rest" until the UK had left the EU, insisting Brexit would happen on 31 October "come what may... do or die".
Meanwhile, the other candidate, Jeremy Hunt has promised to boost defence spending by £15bn over the next five years if he becomes prime minister.
In his interview with BBC political editor Laura Kuenssberg, Mr Johnson said the existing deal negotiated by Theresa May "is dead".
He insisted it was possible to broker a new deal with the EU before the end of October because the political landscape had changed in the UK and on the continent.
"I think actually that politics has changed so much since 29 March," he said, referring to the original Brexit deadline.
"I think on both sides of the Channel there's a really different understanding of what is needed."
At the moment, the UK is due to leave the EU on 31 October after the PM's Brexit deal was rejected three times by Parliament, and the EU has previously said the withdrawal agreement reached with the UK cannot be reopened.
Mr Johnson said he would be able to persuade Brussels to resolve the Irish border issue - a key sticking point - despite repeated warnings from EU leaders that that was impossible.
He said there were "abundant, abundant technical fixes" that could be made to avoid border checks.
When challenged that these did not exist yet, Mr Johnson replied: "Well, they do actually... in very large measure they do, you have trusted trader schemes, all sorts of schemes that you could put into place."
But, he admitted, there was "no single magic bullet" to solve the issue.
Mr Johnson's really controversial gamble is to say he could do a new trade deal with EU leaders before the end of October.
And he says he would be able to do that before resolving the most controversial conundrum - how you fix the dilemma over the Irish border.
He clearly believes he has the political skill to pull that off. He and his supporters would say that is a plan.
But it is a plan that is full of ifs and buts - either heroic or foolhardy assumptions to imagine that EU leaders and Parliament would be ready to back his vision - and back it by Halloween - on an extremely tight deadline.
The political pressure is on, not just to get it done quickly, but done in a way that does not harm our relations with the rest of the world and the livelihoods of people living in this country.
In terms of the controversies over his personal life, it is absolutely clear even now - when he is on the threshold of No 10 - that Boris Johnson thinks there are questions he simply does not have to answer.
And for a politician about whose character many people have their doubts, that is going to follow him around unless and until he is willing to give more.
Mr Johnson said if he was elected he would start new talks as soon as he reached Downing Street to discuss a free trade agreement.
He also said he hoped the EU would be willing to grant a period of time where the status quo was maintained for a deal to be finalised after Brexit.
He called this "an implementation period", but accepted this was not the same as the implementation period in the current draft treaty agreed with the EU.
Mr Johnson committed to passing new laws as soon as possible in order to guarantee the rights of EU citizens living in the UK.
The former foreign secretary also suggested EU leaders might change their attitude to renegotiation because they had Brexit Party MEPs they did not want in their Parliament, and wanted to get the £39bn that had been promised as part of the so-called divorce bill.
And he said MPs could be more willing to back a revised deal because - after disappointing local and European elections last month - they realised both Labour and the Conservatives would face "real danger of extinction" if Brexit were to be stalled again.
Mr Johnson refused again to give more detail of what happened at his home in the early hours of Friday.
"I do not talk about stuff involving my family, my loved ones," he said.
"And there's a very good reason for that. That is that, if you do, you drag them into things that really is... not fair on them."
Instead of his private life, he said the public actually want to know "what is going on with this guy?"
"Does he, when it comes to trust, when it comes to character, all those things, does he deliver what he says he's going to deliver?"
Despite widespread criticisms from his fellow Conservatives that he cannot be trusted, Mr Johnson said anyone questioning his character was "talking absolute nonsense".
He also refused to respond to accusations from rival Jeremy Hunt that he was being a "coward" for avoiding more head-to-head TV debates, promising that if elected he would "govern from the centre right" because the centre "is where you win".
Ms Rudd, who is supporting Mr Hunt, said Mr Johnson was making a mistake by shying away from the debates and said he needed to "go further" in explaining his Brexit plan.
"This is an incredibly difficult situation and Boris needs to explain how he will deal with both sides of the Conservative Party that have concerns and try and break the impasse with the European Union.
"Enthusiasm and optimism is not sufficient."
Responding to claims that a dozen Tory MPs would be prepared to bring down a government heading to a no-deal Brexit, she said: "I think that's about right. I think it's slightly less than that, but it's certainly more than two."
Correction 7th August 2019: An earlier version of this article referred to crippling tariffs on trade in the event of a no-deal Brexit and has been amended to make clear that Boris Johnson was asked about this as a possibility.

Boris Johnson says the government is "working together" and that he will not be resigning after criticism of his intervention on Brexit.
The foreign secretary has been accused of undermining Theresa May with a 4,000-word article setting out his own post-EU vision.
But he told journalists the government was "a nest of singing birds".
Mr Johnson - along with other ministers - is due to attend the PM's Brexit speech in Florence on Friday.
Asked about his article, Mrs May said she was "getting on with the job" of delivering Brexit.
Earlier the foreign secretary was accused by ex-chancellor Ken Clarke of making a pitch for a future Tory leadership election with his article.
Mr Clarke said that "in normal circumstances" Mr Johnson would have been sacked. Some reports have claimed Mr Johnson will resign if his blueprint for Brexit is not followed.
But speaking in New York, the foreign secretary said "of course not" when asked whether he was going to quit, and predicted the government would "deliver a fantastic Brexit".
Asked whether there was a cabinet split on Europe, Mr Johnson said: "No, we are a government working together.
"We are a nest of singing birds."
Mr Johnson and Mrs May are both attending the United Nations General Assembly in New York.
Asked repeatedly about Mr Johnson and reports of cabinet disunity over Brexit, the PM stressed that the government was united in trying to get the best possible deal.
"What I think the majority of the British public want to see is what we're doing, which is getting on with the job of those negotiations with the European Union and getting on with the job of the best deal for the UK," she told the BBC.
Responding to questions about the so-called divorce bill for the UK to pay on leaving the EU, she said the UK was a "law-abiding nation" and would "stand by our obligations" as well as carrying on contributing to programmes it wants to be a part of after Brexit.
Mr Johnson's article said the UK should not pay for access to the EU single market.
The continuing fallout from the article - published in Saturday's Telegraph - led, on Monday, to Mrs May having to rebut claims that Mr Johnson was trying to become a "back-seat driver" in her cabinet.
The PM, who is due to set out her vision for Brexit in a speech in Florence on Friday, declared: "This government is driven from the front."
Speaking on BBC Radio 4's Today programme, Mr Clarke said that in her speech Mrs May had to set out "for the first time, really" what the UK can "can realistically achieve in negotiations".
That must include "free access to the European market and no new barriers for our trade," he argued, and how best "to avoid economic damage to the country".
"Alongside that, personal publicity and campaigning by the foreign secretary is actually just an irrelevant nuisance."
Mr Clarke said: "Sounding off personally in this way is totally unhelpful and he shouldn't exploit the fact she hasn't got a majority in Parliament.
"He knows perfectly well that normally the foreign secretary would be sacked for doing that - and she, unfortunately, after the general election, is not in the position easily to sack him - which he should stop exploiting."
He also attacked Mr Johnson for repeating "one of the more simplistic and dishonest arguments of the hardline Leavers" in his article - a reference to "taking back control" of £350m a week after Brexit.
The foreign secretary said on Monday that his article was meant to be an "opening drum roll" for the PM's speech.
"Because I was involved in that Brexit campaign, people want to know where we are going," he added.
Mrs May attempted to avoid a public row with her foreign secretary, telling reporters travelling with her on a trade mission to Canada: "Boris is Boris."
Former foreign secretary, Lord Hague, writing in the Daily Telegraph, warned that disunity over Brexit could hand power to Jeremy Corbyn's Labour Party.
He wrote: "It is putting it a bit too politely to say, in the wake of Boris Johnson's article in this newspaper on Saturday, that the approach of senior ministers to the Brexit negotiations appears to lack co-ordination.
"More bluntly, it is now 15 months since the referendum, and high time that all members of the government were able to express themselves on this subject in the same way as each other, putting forward the same points, as part of an agreed plan."

Boris Johnson has likened the challenge of avoiding a hard border in Northern Ireland to the boundaries between different boroughs of London.
The foreign secretary said it was a "very relevant comparison" because money was "invisibly" taken from people travelling between Camden and Westminster when he was London mayor.
London's congestion zone charge does not involve manual checks.
Labour said his comments were "typically facile and tactless".
The Irish opposition Fianna Fail party said it was "extraordinary" to suggest the two borders were the same, while the SDLP said: "Trivialising the very serious concerns relating to Ireland displays a dangerous ignorance that must be challenged."
The future of the Irish border after Brexit has been a key sticking point in talks so far.
The UK plans to leave the EU's customs union but wants to avoid border posts and physical checks between Northern Ireland and the Republic.
Mr Johnson, a former London mayor, told BBC Radio 4's Today programme there were "all sorts of things you can do" to achieve this.
"We think that we can have very efficient facilitation systems to make sure that there's no need for a hard border, excessive checks at the frontier between Northern Ireland and the Republic," he said.
"There's no border between Islington or Camden and Westminster... but when I was mayor of London we anaesthetically and invisibly took hundreds of millions of pounds from the accounts of people travelling between those two boroughs without any need for border checks whatever."
He added: "It's a very relevant comparison because there's all sorts of scope for pre-booking, electronic checks, all sorts of things that you can do to obviate the need for a hard border to allow us to come out of the customs union, take back control of our trade policy and do trade deals."
Analysis by the BBC's Mark Devenport
How literally should we take the Foreign Secretary's analogy? The collection of the London congestion charge relies on a network of automatic number plate recognition cameras which identifies motorists moving around the city.
However back in August last year, when the UK released a position paper on Northern Ireland after Brexit, government officials briefed journalists that a pledge to "avoid any physical border infrastructure in either the United Kingdom or Ireland, for any purpose (including customs or agri-food checks)" effectively ruled out plans for the installation of cameras near the border, or set back from it.
Instead the clear suggestion was that any technological fix would be more likely to involve firms becoming "authorised economic operators" and filling out customs forms from the comfort of the desks in their office HQs.
The BBC has asked for clarification of whether government policy has shifted on this point. But in the absence of a more detailed response we may note that Downing Street has told lobby correspondents that Mr Johnson "was not offering a technical solution" to the border issue.
Instead, the prime minister's spokesman clarified, "the foreign secretary was making a comparison to demonstrate our overall approach that the 110 million people crossing the border will continue living their lives as before, travelling freely just as Londoners cross boroughs every day".
That defence is not likely to appease Mr Johnson's critics, but it seems fair to say he was trying to get out of a tight spot during a wide ranging Today programme interview, rather than seeking to unveil a wholly new approach to the one set out in last year's position paper.
Labour's shadow Northern Ireland secretary Owen Smith dismissed the comments as "ludicrous".
And he accused Mr Johnson of "glibly dismissing the concerns of thousand of families and businesses who live and work along the border", adding that his remark "insults the intelligence of all who are worrying about how to resolve the border question after Brexit".
Irish MEP Mairead McGuinness, vice president of the European Parliament, also questioned the analogy. "The UK is a different country than the Republic of Ireland ... and therefore the comparison doesn't quite fit," she told BBC2's Daily Politics.
The foreign secretary's comments have also sparked a wave of reaction on Twitter:
But former Conservative leader Iain Duncan Smith backed Mr Johnson.
"What Boris was saying was there are various ways in which you can manage things, like money transfers, checks on cars, checks on lorries - the technology now exists and is being used and is being developed around the world," he told BBC Radio 4's The World at One.
And DUP MP Sammy Wilson said a virtual border already exists.
"There's a different tax regime in Northern Ireland than the Irish Republic - VAT, excise duty is different - yet billions of pounds worth of goods cross that border, taxes are paid and not a lorry is stopped to check the goods because through virtual methods, through IT, through electronic invoicing, those taxes are collected by both the Irish government and the British government," he said.
The first draft of a legally-binding agreement between the UK and the EU, due to be published on Wednesday, is expected to address the issue of Northern Ireland.
The Dublin government says the option of Northern Ireland staying in full regulatory alignment with the European Union after Brexit should be included as a "backstop" - but this is opposed by some Conservative MPs and the Democratic Unionist Party.
Meanwhile former World Trade Organisation chief Pascal Lamy argued that whatever Brexit option was chosen "will necessitate a border" between Northern Ireland and the Republic, because checks will have to be carried out on goods and people.
Instead he suggested to the Commons Brexit committee a "Macau option" for Northern Ireland.
"You should think about giving to Northern Ireland the same autonomous trade capacity that China has given to Macau, which doesn't mean that Macau doesn't belong to China," he said.

The prime minister has said it is "up to the EU, this is their call" if the UK leaves the EU without a deal.
Boris Johnson made his first visit to Wales as PM on Tuesday, seeking support from farmers for his Brexit plans.
He held talks with Wales' First Minister Mark Drakeford, who said there was a "deeply concerning lack of detail" from the new prime minister.
Mr Johnson said: "We're not aiming for a no-deal Brexit, we don't think that's where we'll end up."
"This is very much up to our friends and partners across the channel," he added.
A Welsh farmer called on Mr Johnson to stop "playing Russian roulette" with the lamb industry over the threat of a no-deal Brexit.
It followed the Farmers' Union of Wales president warning of "civil unrest" in rural areas if no agreement is struck.
Earlier, the prime minister had his first phone call with Irish leader Leo Varadkar since taking office.
The visit to Wales came as the Conservatives fight to hold Brecon and Radnorshire in a by-election on Thursday.
Mr Johnson visited a chicken farm in St Brides Wentlooge, near Newport, before travelling to online retailer BVG Group in Brecon.
He later attended a meeting in the Welsh Assembly with Mark Drakeford, where he was booed by a group of protesters on arrival.
In a news conference afterwards, Mr Drakeford said they had an "engaged discussion" on Brexit.
The Welsh Labour leader said he pressed Mr Johnson to explain the path to a deal with the EU but did not get a "clear sense" from him of what the plan would be.
Mr Drakeford said he emphasised the "catastrophic effect" a no-deal Brexit would have on the Welsh economy, and said the PM provided assurances of support for manufacturing and agriculture in such a scenario.
"But asked to describe the nature of that support, I'm afraid that there is a deeply concerning lack of detail that is available to people whose livelihood is on the line," Mr Drakeford said.
The first minister said the PM told him there would be many new opportunities for Welsh agriculture and businesses, but he had "no sense again" there was detailed thinking behind what "otherwise becomes vacuous optimism".
Mr Drakeford said he warned Mr Johnson "the future of the UK is more at risk today than at any other point in his political lifetime", and said he had put ideas to him on how the Union could be "reinvented".
A Downing Street spokeswoman said the two spoke about the importance of the union and support for farmers in Wales.
She added: "The PM set out how the UK will be leaving the EU on October 31st, come what may, and said he would seek to work with the Welsh Government and other devolved administrations, to make sure communities across the UK are ready to maximise on the opportunities that Brexit will bring."
Many Welsh farmers are heavily reliant on free trade with the EU. If the UK leaves without a deal many would face significant tariffs on their exports to EU countries.
The prime minister did not give any television interviews to Welsh broadcasters on Tuesday.
However, during the farm visit, he told reporters the agriculture sector will "have the support they need" in the event of no-deal.
"We will make sure that they have the support that they need, if there are markets that are going to be tricky that we help them to find new markets, we have interventions that aim to support them and their incomes," Mr Johnson said.
"The most important point is that we don't want tariffs and we don't envisage they will be necessary.
"And I think common sense would dictate it would be better and massively in the interests of our EU friends to have a zero-tariff, zero-quota regime of the kind we currently have."
Mr Johnson suggested funds for "export refunds" would be made available for the Welsh Government to administer.
Asked how the system would work, given agriculture is devolved, he said: "It will be up to the Welsh Government to administer it. We will make sure the funds are available."
A Welsh Government source said they were surprised by the nature of the announcement.
The farming industry is worth more than £6bn to the Welsh economy and supports 14,000 businesses, 45,000 jobs and about 25,000 farmers.
Welsh lamb will face at least 40% tariffs in a no-deal scenario, prompting a sheep farmer to call for Mr Johnson "to stop playing Russian roulette with the industry as he appears to be doing at the moment".
"If we do go out with a no deal, it will be absolutely catastrophic even if it is just for a few months," Helen Roberts, who is also development officer for the National Sheep Association in Wales, told Radio 4's Today programme.
She said her members would protest against a no-deal Brexit, adding: "I think it's time to come and stand up for ourselves, and be counted."
On Monday, the prime minister said there was "every chance" a Brexit deal with the EU could be struck, but the existing agreement with the EU has "got to go".
However senior minister Michael Gove, who has been put in charge of preparing for no deal, has said the UK government was working on the assumption the UK would leave the EU without an agreement.
Ahead of his meeting with Mr Johnson, Mr Drakeford tweeted Brexit "will decimate our agricultural and manufacturing sectors and risks ripping the Union apart".
"The PM must stop playing fast and loose with our country," he said.
Earlier on Tuesday, Welsh Secretary Alun Cairns suggested new global markets, including in Japan, will be available to sheep meat producers.
Mr Cairns told the BBC: "We are now looking to the growth that will come from right around the world, 90% of global growth will come from outside of the EU,
"But we don't want to close our back on the European market either and that's why working hard to get a deal is important, but of course there needs to be a shift in attitude and a positive response to the cause that we're making."
Plaid Cymru Westminster leader Liz Saville Roberts pointed out via Twitter the Japanese market had been opened up to Welsh lamb by the EU-Japan trade deal.
Mr Cairns added farmers "can be guaranteed that the same money will be available to ensure that we are protecting this sector".
By Felicity Evans, BBC Wales political editor
It is clear there was no meeting of minds between Mark Drakeford and Boris Johnson.
As well as having "fundamentally different views" on Brexit, the two leaders are very different characters.
The first minister is a details man - after Brexit he wants to know what support will be on offer to Welsh manufacturing and agriculture, when it'll be available and how long for.
But the prime minister paints in bold colours, and he knows that despite concerns over the impact of a no-deal exit in Wales, voters here chose to leave the EU in 2016.
This is the first of many meetings between the two leaders - whether they can find common ground remains to be seen.

Boris Johnson has given key cabinet roles to leading Brexiteers after becoming the UK's new prime minister.
Dominic Raab and Priti Patel return to government as foreign secretary and home secretary respectively.
Sajid Javid has been named as the new chancellor as more than half of Theresa May's old cabinet, including leadership rival Jeremy Hunt, quit or were sacked.
Earlier, Mr Johnson said the Brexit "doomsters and gloomsters" were wrong and the UK would leave on 31 October.
Speaking outside No 10, he said the UK would meet that deadline "no ifs, no buts", adding: "The buck stops with me."
Mr Johnson then turned his attention to a radical overhaul of the government, with 17 of Mrs May's former senior ministers being axed or stepping down.
Announcing his departure, Foreign Secretary Mr Hunt said he had been offered an alternative role but had turned it down.
Defence Secretary Penny Mordaunt, a leading Brexiteer who is popular across the party, was the most surprising departure. She has been replaced by Ben Wallace, a former soldier and longstanding ally of Mr Johnson's.
Another prominent Brexiteer, International Trade Secretary Liam Fox, was also ousted, along with Business Secretary Greg Clark - a vocal opponent of a no-deal Brexit.
All three supported Mr Hunt in the Tory leadership contest.
Education Secretary Damian Hinds, Northern Ireland Secretary Karen Bradley, Immigration Minister Caroline Nokes, Culture Secretary Jeremy Wright and Communities Secretary James Brokenshire have also gone, along with Chris Grayling, whose record as Transport Secretary was much criticised.
Scottish Secretary David Mundell, who has left his position after four years, joked whether there would be "room" on the backbenches after all the dismissals.
This comes on top of the earlier resignations of four leading ministers, including Chancellor Philip Hammond, Justice Secretary David Gauke and Cabinet Office minister David Lidington.
Conservative MP Nigel Evans described the changes as a "summer's day massacre".
The BBC's chief political correspondent Vicki Young said the sackings suggested Mr Johnson wasn't looking to build bridges across the party.
Instead, she said, he was focused above all else on assembling the team he thought would bring about the results he needed, even if that was controversial.
As the upheaval in government was happening, hundreds of people gathered outside the gates of Downing Street in protest against Mr Johnson's appointment.
Former Home Secretary Sajid Javid - a banker before entering politics - has been given the key role of chancellor, having thrown his weight behind Boris Johnson after being eliminated from the leadership race himself.
Priti Patel - who quit as international development secretary in 2017 after holding unauthorised meetings with Israeli officials - succeeds Mr Javid at the Home Office, where she said she would focus on keeping the UK country safe and fighting "the scourge of crime".
Dominic Raab is a former Brexit secretary, but quit over Mrs May's handling of the process.
He said he was "hugely humbled" by his appointment and said the UK needed to "bring finality" to Brexit so it could focus on the other big challenges.
Other figures involved in the Vote Leave referendum campaign have also been rewarded.
Michael Gove leaves behind his environment brief to become Chancellor of the Duchy of Lancaster, a more senior ministerial role but one without a specific portfolio.
Meanwhile, Jacob Rees-Mogg becomes leader of the House of Commons - his first government role.
Liz Truss moves from second in command at the Treasury to head the Department for International trade while Steve Barclay has been re-appointed as Brexit Secretary.
Health Secretary Matt Hancock and Work and Pensions Secretary Amber Rudd are among the few ministers who backed Remain who have kept their jobs. Ms Rudd also takes on the women and equalities brief.
Meanwhile, there is a speedy return to office for Gavin Williamson as education secretary.
He was sacked as defence secretary less than three months ago after No 10 concluded he was responsible for the leaking of unauthorised information from a National Security Council meeting - which he denied.
Mr Johnson's team has promised a record number of women in the cabinet. Nicky Morgan, Theresa Villiers and Andrea Leadsom have all returned to top jobs, taking on the culture, environment and business briefs respectively.
There are also promotions for Robert Buckland (justice) and Alok Sharma (international development) while former party chairman Grant Shapps, a key member of Boris Johnson's leadership campaign team, makes a comeback at transport.
Former Chief Whip Julian Smith is the new Northern Ireland Secretary, while Dumfries and Galloway MP Alister Jack, who was only elected to Parliament last year, is expected to become Scottish Secretary. Alun Cairns remains as Welsh Secretary.
Earlier, in a 13-minute speech outside Downing Street, Mr Johnson listed a wide range of domestic ambitions, chiefly a promise to sort out care for the elderly "once and for all".
Reforms to the social care sector have eluded previous governments because of their cost and complexity.
"We will fix it once and for all with a clear plan we have prepared to give every older person the dignity and security they deserve," he insisted.
Mr Johnson also pledged to improve infrastructure, recruit 20,000 new police officers and "level up" school spending. He promised reforms to ensure the £20bn in extra funding earmarked for the NHS "really gets to the front line".
And he pledged to boost the UK's biotech and space science sectors, change the tax rules to provide incentives for investment, and do more to promote the welfare of animals.
Setting out his priorities for office, the former London mayor hit out at the "pessimists" who did not believe Brexit could be delivered and called for an end to three years of indecision.
"The people who bet against Britain are going to lose their shirts because we are going to restore trust in our democracy," he said.
"The time has come to act, to take decisions and change this country for the better."
He said he had "every confidence" the UK would leave the EU in 99 days time with a deal, but preparations for the "remote possibility" of a no-deal Brexit would be accelerated.
Mr Johnson vowed to bring all four nations of the United Kingdom - or what he described as the "awesome foursome" - together in the task of strengthening a post-Brexit country.
"Though I am today building a great team of men and women, I will take personal responsibility for the change I want to see," he concluded.
"Never mind the backstop, the buck stops here."
Labour's Sir Keir Starmer said Mr Johnson's speech was "all rhetoric". New Lib Dem leader Jo Swinson said she would welcome a cross-party push to find a solution on social care, but attacked Mr Johnson's "bluster and bravado" over Brexit.
Mr Johnson took over after Theresa May handed in her resignation to the Queen.
Earlier, as she relinquished power after three years, Mrs May said being prime minister had been "the greatest honour" and wished her successor well.
During his journey to Buckingham Palace, Mr Johnson's car was briefly held up by protesters from Greenpeace, who formed a human chain across The Mall.

Boris Johnson has restored the whip to 10 of the 21 Tory MPs who rebelled against him over Brexit last month.
The rebels were expelled from the parliamentary Conservative Party after backing efforts to pass legislation to block a no-deal Brexit.
Ex-ministers including Ed Vaizey and Margot James are among those to be welcomed back.
Former Tory chancellors Philip Hammond and Ken Clarke are among those who remain outside the party.
The move to readmit the rebels came shortly before MPs backed the prime minister's plan to hold an early general election on Thursday, 12 December.
Those who have had the whip restored are now eligible to stand as Conservative candidates at the election if new candidates have not since been chosen.
Some of those who have been welcomed back, including Sir Nicholas and former minister Alistair Burt, have previously said they would be retiring.
As well as Sir Nicholas, grandson of Sir Winston Churchill, those readmitted into the party include Greg Clark, who served as a cabinet minister under Theresa May.
Caroline Nokes, Richard Benyon, Stephen Hammond, Steve Brine and Richard Harrington complete the list of those to have been given the whip back.
Ex-chancellors Philip Hammond and Ken Clarke, and former justice secretary David Gauke, are among those not to have had the whip restored.
Sir Oliver Letwin, Justine Greening, Dominic Grieve, Rory Stewart, Guto Bebb, Anne Milton and Antoinette Sandbach also remain as independents.

Boris Johnson has pledged to "hold out the hand" and "go the extra thousand miles" to strike a new Brexit deal.
During a visit to Scotland, the prime minister said the existing withdrawal agreement negotiated with European leaders was "dead" and had "got to go".
However, he said there was "every chance we can get a deal".
But Scotland's First Minister, Nicola Sturgeon, said Mr Johnson had set the UK on an "almost inevitable path to a no-deal Brexit".
Preparations for leaving the European Union without a withdrawal deal are being ramped up, with Mr Johnson saying the UK must leave the EU by 31 October.
While in Scotland he met Ms Sturgeon and Scottish Conservative leader Ruth Davidson - both of whom have positioned themselves against a no-deal exit.
Two committees have been set up as the UK government intensifies preparations for a possible no-deal exit, including a "daily operations committee" of senior ministers.
Meanwhile, the pound has sunk to a 28-month low against the dollar, apparently due to concerns about Brexit.
Speaking at the Faslane naval base near Glasgow, Mr Johnson said his "assumption is that we can get a new deal", but said it was "responsible for any government to prepare for no deal if we absolutely have to".
He said: "I don't want the UK to be aloof or hanging back, I want us to engage, to hold out the hand, to go the extra thousand miles, and what we want to do is make it absolutely clear that the backstop is no good, it's dead, it's got to go.
"The withdrawal agreement is dead, it's got to go. But there is scope for us to do a new deal.
"We will make it very clear to our friends - we're talking to the Irish today - what the limits are and what we want to do.
"We're very confident that with goodwill on both sides, two mature political entities, the UK and EU, can get this thing done."
Meanwhile, the prime minister's chief Brexit negotiator, David Frost, has urged his EU counterparts not to "underestimate" Mr Johnson or his commitment to the 31 October deadline.
Mr Johnson has faced scrutiny over his Brexit strategy from colleagues and opponents alike during his visit to Scotland.
Ms Davidson has previously said Mr Johnson has her "full support" in his efforts to secure a withdrawal agreement with the EU, but that she will not support a no-deal Brexit.
After a meeting at Holyrood, the Scottish Tory leader said the pair had discussed their "shared determination to strengthen the Union", adding Mr Johnson had "made clear the government's preference is to leave the EU with a deal".
Mr Johnson, meanwhile, said he was Ms Davidson's "number one fan".
Analysis by BBC Scotland editor Sarah Smith
Boris Johnson's toughest meeting might not have been with Scottish First Minister Nicola Sturgeon, but rather Scottish Conservative leader Ruth Davidson.
Ms Davidson made no secret of the fact that she did not want Mr Johnson as PM. And in the few days since he took charge relations have already gone further south.
He ignored his Scottish leader's advice not to sack the Scottish Secretary David Mundell and replace him with the pro-Brexit MP Alister Jack. He then further snubbed the Scottish contingent of parliamentarians when he put an MP who sits for an English seat into the Scotland office as a minister.
Ms Davidson has said publicly that she would not support a no-deal exit from the EU and that as leader of the Scottish party she does not have to sign up to any loyalty pledge to support a no deal.
She believes the PM would have sacked her if he could. But he can't - and she will take full advantage of her ability to speak out.
Ms Sturgeon - who hosted Mr Johnson at her official Bute House residence - has also pledged to fight against a no-deal exit, saying it would cost 100,000 jobs and "plunge the economy into recession".
Speaking after what she described as a "very lively exchange" with Mr Johnson, she also said she believed he was really pursuing a no-deal Brexit.
"He says he wants to get a deal, but what is not clear to me is how he intends to get from the very hard-line, fixed position that he's taken to a position where a deal is possible, if the EU also sticks to the very consistent position it has taken," she said.
"That makes me think that whatever Boris Johnson is saying about his preference being to strike a deal, in reality he is pursuing a no-deal Brexit."
She added that she had made clear to Mr Johnson her opposition to Brexit and no-deal and that the people of Scotland should be able to "choose their own future".
A No 10 spokesman said the PM told Ms Sturgeon he "was a passionate believer in the power of the Union" and "would work tirelessly to strengthen the United Kingdom and improve the lives of people right across Scotland".
Mr Johnson said his preference was to negotiate a new deal that abolished the backstop - but the UK would be leaving the EU on 31 October "come what may", the spokesman added.
Mr Johnson also used his trip to Scotland to announce funding for projects to boost the economy in Scotland, Wales and Northern Ireland.
However Scottish Finance Secretary Derek Mackay claimed the £300m "isn't new funding" and was already under negotiation before Mr Johnson became prime minister.
Welsh Labour also hit out at the funding plans, calling them "very thin stuff" which would not make up for a "chronic lack of investment".
The UK government, however, insisted the money was new, with Scottish Secretary Alister Jack saying city deals would help "create jobs and boost local economies".
The growth deal plan comes after Mr Johnson announced a £3.6bn towns fund over the weekend, which will initially support 100 places in England.
As part of his visit to Scotland, the prime minister also announced plans for a new Office for Veterans' Affairs within the UK government, to coordinate medical treatment and training and "ensure no veteran is disadvantaged because of their service".
The prime minister also plans to go to Wales to meet members of its farming community and Northern Ireland to discuss ongoing efforts to restore devolution at Stormont.
Who is in charge of what?

The government's final Brexit proposals will include customs checks on the island of Ireland.
The BBC's Laura Kuenssberg said Boris Johnson's plans will see Northern Ireland "in a different relationship with the EU to the rest of the UK".
Boris Johnson is addressing the Tory conference before submitting the new proposals to the EU.
The European Commission said they will "examine it objectively" and "listen carefully to the UK".
The Commission's president, Jean-Claude Juncker will talk to the PM on the phone later, while negotiating teams will meet in Brussels.
In his first speech at the event as prime minister, he will call it a "fair and reasonable" Brexit compromise, and say only by leaving the EU on 31 October can the UK "move on".
Mr Johnson will also claim the public will no longer be "taken for fools" by those who want to delay or block the process.
Tory Chairman James Cleverly said the UK had been "flexible and pragmatic", and now the EU must be the same.
On the eve of his speech, Mr Johnson told a conference fringe meeting in Manchester, hosted by the DUP, that he hoped to reach a deal with the EU over the course of "the next few days".
The government has insisted it will not negotiate a further delay beyond the Halloween deadline, saying this would be unnecessary and costly for the UK.
However, under the terms of a law passed by Parliament last month, the PM faces having to request another extension unless MPs back the terms of withdrawal by 19 October - two days after a summit of European leaders.
On Tuesday, Mr Johnson dismissed leaked reports that customs posts could be set up on either side of the border between Northern Ireland and the Republic of Ireland.
He said suggestions the UK wanted "clearance zones" for goods as part of a package of alternative arrangements to replace the Irish backstop were wide of the mark.
While he conceded some customs checks would be needed as the UK leaves the EU's customs union and single market, he said technology could keep them to an "absolute minimum".
The issue of the Irish border - and how to keep it free from border checks when it becomes the frontier between the UK and the EU - has been a key sticking point in Brexit negotiations.
Mr Johnson says the solution reached by the EU and Theresa May, the backstop, is "anti-democratic" and "inconsistent with the sovereignty of the UK", claiming it offered no means for the UK to unilaterally exit and no say for the people of Northern Ireland over the rules that would apply there.
BBC political editor Laura Kuenssberg said the new offer from Mr Johnson included some new customs checks on the island of Ireland, and would leave Northern Ireland in a different relationship with the EU to the rest of the UK in some ways.
She said the plans were "based on the notion of consent", giving more powers to Northern Ireland's devolved Parliament - the Stormont Assembly - to shape its future relationship with the EU - despite the fact the assembly is approaching 1,000 days without sitting.
The proposals also suggest a time period for when the relationship between Northern Ireland and the EU could move on.
But the full and precise details of Mr Johnson's plan twill not be clear until after the prime minister's speech at conference.
Speaking to BBC Radio 4's Today programme earlier, Mr Cleverly appeared to put the ball in the EU's court.
"We have been in negotiating for some while," he said. "The UK has been flexible, but a negotiation means both parties need to be flexible.
"What we need to see now is the EU be flexible - and if they can be pragmatic and flexible, we can leave with a deal on 31 October. But we are going to leave on 31 October whatever."
Irish Fine Gael senator Neale Richmond told Today that the PM's plans were a "big move" from the withdrawal agreement made by Theresa May.
Mr Richmond said, under the plan, Northern Ireland would leave the customs union and "come out of the single market in all areas, apart from agri-food products and industrial products, and indeed it only stays in those areas for four years".
This, he added, would require "additional checks" on the island of Ireland - something he described as "extremely disappointing".
Laura Kuenssberg said there was a "real expectation and belief" in No 10 that "this is now the crunch point".
She said: "This is the moment…where the EU will have to respond and say [either] there is something that is a basis of a deal here, or not.
"And what Boris Johnson is trying to suggest is if the answer is not, then for him, that means no-deal."
The EU needs to see the precise details of Boris Johnson's proposals, but the direction of travel that has been coming through is different.
The very idea of customs check between Ireland and Northern Ireland, the promise of the use of technologies to ease the process that haven't yet been tried and tested, or don't even exist yet…that is a big no-no for the EU.
The bloc will look at the proposals carefully. They need to try as they do want a deal, and also they need to be seen to be trying.
But it is fundamentally misunderstanding the EU if the prime minister thinks at this stage the 26 EU leaders will turn round on the Irish prime minister and say: "Listen, you are going to have to accept this because we just want to have a deal."
It is also fundamentally misunderstanding the German Chancellor Angela Merkel, her attachment to EU unity and the integrity of the single market.
And also it is misunderstanding that the EU sees this in a bigger picture. If suddenly now they were to back down to all of the prime minister's demands how would that look to other trade partners across the globe.
So EU leaders will be very careful not to rubbish the prime minister's ideas, to talk about them as a basis for an agreement, but if it is take it or leave it, they will be leaving at this point.
BBC assistant political editor Norman Smith said it was particularly important Mr Johnson secured the support of the Democratic Unionist Party's 10 MPs.
He said: "I think it is very clear this deal is not going to fly unless Boris Johnson can bring the DUP along with him... one way or another he has to make sure they're on board."
BBC Northern Ireland political editor Mark Devenport said sources from the DUP were supportive of the proposals and had been kept informed during their development.
However, the party's leader, Arlene Foster, declined to say whether she had seen the PM's proposals.
She told the BBC: "What we are doing with this prime minister is working very closely with him and we will continue to work closely with him over the next couple of hours and days.
"I hope we do get a deal that is acceptable to the European Union and one that is good for the whole of the United Kingdom."
Speaking in Manchester, Mr Johnson will suggest voters are "desperate" for the country to focus on other priorities and will contrast his determination to leave on 31 October with the "years of uncertainty" that he says would result from a Labour government promising another referendum.
"What people want, what Leavers want, what Remainers want, what the whole world wants - is to move on," he is expected to say.
"I am afraid that after three-and-a-half years people are beginning to feel that they are being taken for fools.
"They are beginning to suspect that there are forces in this country that simply don't want Brexit delivered at all.
"And if they turn out to be right in that suspicion then I believe there will be grave consequences for trust in democracy.
"Let's get Brexit done on October 31 so in 2020 our country can move on."
Mr Johnson's conference speech is set to clash with Prime Minister's Questions, which is taking place at 12.00 BST.
Normally the Commons goes into recess for the Tory conference, but MPs voted against this amid the bitter fallout from the government's unlawful prorogation of Parliament.
Foreign Secretary Dominic Raab will deputise for the prime minister, facing the shadow home secretary Diane Abbott over the despatch box.
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Boris Johnson has secured the highest number of votes in the first MPs' ballot to select the Conservative Party leader and next prime minister.
Three contenders - Mark Harper, Andrea Leadsom and Esther McVey - were knocked out in the secret ballot of Tory MPs.
Mr Johnson received 114 votes, significantly more than his nearest rival Jeremy Hunt, who came second with 43. Michael Gove was third with 37.
Seven candidates progress to the next round of voting next week.
The two who prove most popular after the last MPs' ballot will go to Conservative Party members in a final vote later this month.
The winner of the contest to succeed Theresa May is expected to be announced in the week of 22 July.
Sources close to Health Secretary Matt Hancock told the BBC's Laura Kuenssberg he was "mulling over" whether to withdraw from the contest after coming sixth with 20 votes.
Home Secretary Sajid Javid, who came fifth with 23 votes, is understood to be staying in the race for now. Some have suggested his candidacy - with support from Mr Hancock - could take on Mr Hunt to become second in the ballot.
Mr Johnson, a former foreign secretary who served for eight years as London mayor, said he was "delighted" to win but warned that his campaign still had "a long way to go".
Foreign Secretary Mr Hunt said: "Boris did well today but what the result shows is, when it comes to the members' stage, I'm the man to take him on."
Environment Secretary Mr Gove said it was "all to play for" and he was "very much looking forward" to candidates' TV debates on Channel 4 on Sunday and on BBC One next Tuesday.
All 313 Conservative MPs voted in the first ballot, including Mrs May, who refused to say whom she had backed.
The fourth-placed candidate, former Brexit secretary Dominic Raab, said he was "proud and honoured" and he had a "good base to build on".
Mr Javid said: "I look forward to continuing to share my positive vision and my plan for uniting the country."
Mr Hancock thanked his supporters, saying it was "terrific to have more votes from colleagues than I could have hoped for".
And International Development Secretary Rory Stewart, the seventh-placed candidate, told the BBC's Politics Live he was "completely over the Moon" to have got through the first vote.
He said he had had only six declared votes ahead of the poll, but "more than three times that" had voted for him in the secret ballot.
The margin of success took his fellow candidates by surprise - but not the core of Boris Johnson's team.
After many, many weeks of private campaigning, introducing Boris Johnson to the world of the spreadsheet, this morning one of his organisers wrote the number 114 and sealed it in an envelope.
At lunchtime, the announcement revealed the controversial former foreign secretary had indeed received exactly that number.
That is not just a marker of the level of Mr Johnson's support but for the sometimes clownish politician, whose reputation has risen and fallen and then risen again, it's a sign that it is different this time.
Justice Secretary David Gauke said Mr Stewart was now the main challenger to Mr Johnson, saying: "He's really in with a chance and the momentum is with Rory."
But Defence Secretary Penny Mordaunt, who is supporting Mr Hunt's campaign, said the foreign secretary was "attractive to many sides of the party because he's a serious individual".
And schools minister Nick Gibb told BBC Radio 4's World at One that Mr Gove was now "best placed as a Brexiteer to challenge the front runner" Mr Johnson in the final.
Further ballots are scheduled to take place on 18, 19 and 20 June to whittle down the contenders until only two are left.
The final pair will then be put to a vote of members of the wider Conservative Party from 22 June, with the winner expected to be announced about four weeks later.
After being knocked out of the contest, Mr Harper, a former government chief whip, said he continued "to believe we need a credible plan that delivers Brexit" in order to "restore trust".
Mrs Leadsom's campaign team said they were "disappointed" but "wish all the other candidates well".
And Ms McVey, who gained nine votes, coming last in the first round of MPs' ballots, said she was "extremely grateful" to those who had supported her.
Televised candidates' debates are scheduled to take place, but not all the remaining seven have confirmed they are taking part.
Work and Pensions Secretary Amber Rudd, who is backing Mr Hunt, urged them to appear, saying the Conservative Party "needs to remember that we're not just choosing a leader, we're choosing a prime minister and the public need to see them".
And former Brexit secretary David Davis, who is backing Mr Raab, said it was "very important" for the public to hear from the contenders.
Mr Johnson has previously been criticised by some of his rivals for not taking part in media interviews during the campaign.
The leadership race has so far been dominated by Brexit and arguments over whether a deal can be renegotiated with the EU by 31 October, and whether talking up a no-deal Brexit is a plausible promise.
On Tuesday 18 June BBC One will host a live election debate between the Conservative MPs still in the race.
If you would like to ask the candidates a question live on air, use the form below. It should be open to all of them, not a specific politician.
Tory leadership rivals face first party vote
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Boris Johnson has been elected new Conservative leader in a ballot of party members and will become the next UK prime minister.
He beat Jeremy Hunt comfortably, winning 92,153 votes to his rival's 46,656.
The former London mayor takes over from Theresa May on Wednesday.
In his victory speech, Mr Johnson promised he would "deliver Brexit, unite the country and defeat Jeremy Corbyn".
Speaking at the Queen Elizabeth II centre in London, he said: "We are going to energise the country.
"We are going to get Brexit done on 31 October and take advantage of all the opportunities it will bring with a new spirit of can do.
"We are once again going to believe in ourselves, and like some slumbering giant we are going to rise and ping off the guy ropes of self doubt and negativity."
Mr Johnson thanked his predecessor, saying it had been "a privilege to serve in her cabinet". He was Mrs May's foreign secretary until resigning over Brexit.
The outgoing PM - who is standing down after a revolt by Conservative MPs over her Brexit policy - congratulated her successor, promising him her "full support from the backbenches".
Foreign Secretary Mr Hunt said he was "very disappointed", but Mr Johnson would do "a great job". He said he had "total, unshakeable confidence in our country" and that was a valuable quality at such a challenging time.
Mr Hunt added: "It was always going to be uphill for us because I was someone who voted Remain and I think lots of party members felt that this was a moment when you just had to have someone who voted for Brexit in the referendum.
"In retrospect, that was a hurdle we were never able to overcome."
Donald Trump told an event in Washington "a really good man is going to be the prime minister of the UK now," and Mr Johnson would "get it done", referring to Brexit.
The president added: "They call him Britain Trump. That's a good thing."
Almost 160,000 Conservative members were eligible to vote in the contest and turnout was 87.4%.
Mr Johnson's share of the vote - 66.4% - was slightly lower than that garnered by David Cameron in the 2005 Tory leadership election (67.6%).
The former London mayor and ex-foreign secretary spoke to staff at Conservative Party HQ after his victory was announced.
He was then given a rousing reception by Tory MPs at a meeting in Parliament, where he urged them to "unite, unite, unite and win".
The BBC's Nick Eardley, who was outside the room, said such gatherings had been gloomy and downbeat for many months, but this one was full of laughter.
One MP told our correspondent: "The BoJo show is up and running." Another said: "The cloud has been lifted."
Mr Johnson will begin announcing his new cabinet on Wednesday, but it has already been confirmed that Mark Spencer, MP for Sherwood in Nottinghamshire, will become chief whip - the person responsible for enforcing party discipline in the Commons.
A number of senior figures have already said they will not serve under Mr Johnson, though, citing their opposition to his stance on Brexit.
He has pledged the UK will leave the EU on 31 October "do or die", accepting that a no-deal exit will happen if a new agreement cannot be reached by then.
Education Minister Anne Milton tweeted her resignation just half an hour before the leadership result was due to be revealed, insisting the UK "must leave the EU in a responsible manner".
And International Development Secretary Rory Stewart confirmed he would be returning to the backbenches, where he would be spending more time "serving Cumbria" and "walking".
David Gauke, another vocal opponent of a no-deal Brexit, announced he was resigning as justice secretary.
They join the likes of Chancellor Philip Hammond, Foreign Office minister Sir Alan Duncan and Culture Minister Margot James who have all said they disagree too strongly with Mr Johnson's Brexit strategy to work closely with him.
Boris Johnson will become our next prime minister.
A sentence that might thrill you. A sentence that might horrify you. A sentence that 12 months ago even his most die-hard fans would have found hard to believe.
But it's not a sentence, unusually maybe for politics, that won't bother you either way.
Because whatever you think of Boris Johnson, he is a politician that is hard to ignore.
With a personality, and perhaps an ego, of a scale that few of his colleagues can match. This is the man who even as a child wanted to be "world king".
Now, he is the Tory king, and the Brexiteers are the court.
Read Laura's blog here
The EU Commission's Brexit negotiator, Michel Barnier, said he was looking forward to working with Mr Johnson "to facilitate the ratification of the withdrawal agreement and achieve an orderly Brexit".
The new Tory leader has previously said the agreement Mrs May reached with the EU was "dead", having been rejected three times by MPs.
Guy Verhofstadt, the European Parliament's chief Brexit co-ordinator, said the parliament would hold an extraordinary meeting on Wednesday in response to Mr Johnson's election.
Jeremy Corbyn reacted to the result by tweeting that Mr Johnson had "won the support of fewer than 100,000 unrepresentative Conservative Party members".
"The people of our country should decide who becomes the prime minister in a general election," he added.
Speaking to the BBC later, Mr Corbyn said Labour planned to table a motion of no confidence in Mr Johnson. Asked when that would be, he replied: "It will be an interesting surprise for you all."
Wednesday 12:00 BST onwards: Theresa May takes part in her last Prime Minister's Questions. After lunch she will make a short farewell speech outside No. 10 before travelling to see the Queen to tender her resignation.
Boris Johnson will then arrive for an audience at Buckingham Palace where he will be invited to form a government.
After that he will make a speech in Downing Street before entering the building for the first time as prime minister.
Later, he will begin announcing his most senior cabinet appointments, such as chancellor, home secretary and foreign secretary, and will make and take his first calls from other world leaders.
Thursday: Mr Johnson is expected to make a statement to Parliament about his Brexit strategy and take questions from MPs. Parliament will break up for its summer recess later.
The new PM will also continue announcing his new cabinet.
Newly-elected Lib Dem leader Jo Swinson said Mr Johnson had "shown time and time again that he isn't fit to be the prime minister of our country".
First Minister of Scotland Nicola Sturgeon congratulated Mr Johnson, but said she had "profound concerns" about him becoming prime minister.
The new leader also received congratulations from Arlene Foster, the leader of Northern Ireland's Democratic Unionist Party, whose support has kept the Conservatives in government since the 2017 general election.
She said the pact - known as a confidence and supply agreement - continued and would be reviewed over the coming weeks "to explore the policy priorities of both parties".
Leader of the Scottish Conservatives Ruth Davidson, who backed Mr Hunt in the campaign, also sent her congratulations, adding that the new PM had "an enormous task ahead of him".
In the often divisive Brexit world of "them and us" it's easy to forget that, beyond Brexit, EU leaders still see the UK as a close partner and ally. Today's messages of congratulation to Boris Johnson from across Europe were a timely reminder.
Whatever happens with Brexit, France, Germany, Poland et al still very much hope to work closely with the UK on international issues like Russia sanctions, Iran, and human rights protection.
But EU leaders' welcoming tone does not signal a willingness to accept whatever Prime Minister Johnson might demand in terms of changes to the Brexit deal.
He's right when he says a no-deal Brexit is bad for Brussels, but he overestimates EU wiggle room. Amendments will only be forthcoming if EU leaders deem them workable and are convinced the new prime minister commands a majority in Parliament to get an agreement through once and for all.

The European Union is "open but not convinced" by the UK PM's new proposals for a Brexit deal with the EU, the president of the European Council says.
Donald Tusk was among several leading EU voices to express doubt over Boris Johnson's withdrawal agreement plan.
The plan would keep Northern Ireland in the EU single market for goods but see it leave the customs union.
But what happens to the border between Northern Ireland and Ireland remains a central sticking point.
Irish PM Leo Varadkar said the new plans for the withdrawal agreement were welcome, but "fall short in a number of aspects".
It comes as UK PM Boris Johnson's Europe adviser, David Frost, is to hold another round of talks in Brussels in a bid to break the Brexit deadlock.
The EU's chief negotiator, Michel Barnier, has told European diplomats he still has plenty of questions about the British proposal to replace the backstop - the measure designed to prevent a hard border on the island of Ireland after Brexit.
He has said he will be in a better position to judge possible future negotiations with the UK once he has spoken to Mr Frost.
On Thursday, Mr Johnson said he had made a "genuine attempt to bridge the chasm" with EU officials before time runs out to reach a deal for the 31 October deadline for the UK to leave the EU.
The UK government says it is aiming to reach a final agreement at an EU summit on 17 October.
EU leaders face a delicate political dance, uncertain if Mr Johnson is open for deeper negotiations or is focusing his attention on a possible election campaign, the BBC's Europe editor Katya Adler says.
Whatever happens, she adds, the EU will be reluctant to be seen slamming the door in the face of the UK.
Meanwhile, Scotland's highest civil court is to consider whether Mr Johnson could be jailed if he ignores legislation aimed at preventing no-deal.
The so-called Benn Act requires the government to ask the EU for an extension to the Brexit deadline if it fails to either pass a deal in Parliament, or get MPs to approve no-deal, by 19 October.
However, Mr Johnson has repeatedly insisted he would not ask for a delay as the law requires him to, describing the legislation as a "surrender bill".
Downing Street hopes its new plan will replace the controversial Irish backstop provision that has proved the biggest obstacle to the existing withdrawal agreement.
The backstop was meant to keep a free-flowing border on the island of Ireland but critics - including Mr Johnson - fear it could trap the UK in EU trading rules indefinitely.
Mr Johnson's latest plan seeks to address this with the following:
The new UK proposals envisage two borders - one between Northern Ireland and Ireland, and a second between Northern Ireland and the rest of the UK, says the BBC's Europe editor Katya Adler.
EU negotiators say they have already identified problems with the plans, including the continuing failure to avoid a hard border on the island of Ireland and the threat to the single market.
Donald Tusk reacted in a tweet, after speaking to Taoiseach (Irish prime minister) Leo Varadkar, who is seen as key to agreeing to a withdrawal deal.
For his part, Mr Varadkar voiced concerns over the customs proposals, questioning how Northern Ireland and Ireland could operate under different customs systems without the need for physical checkpoints.
He also questioned the plan to give Northern Ireland's Assembly a veto over entering into a "regulatory zone" with the EU, without the involvement of Ireland or the EU.
The UK has made some progress but "further work is needed", European Commission chief Jean-Claude Juncker said.
Accepting the current proposals would not meet the objectives of the backstop including preventing a hard border, he added.
Meanwhile, the European parliament's Brexit co-ordinator, Guy Verhofstadt, called the plans "unworkable".
In an interview with the BBC, Mr Verhofstadt said the plan represented "a repackaging of old ideas".
Earlier, the European parliament's Brexit committee said the plan didn't match "even remotely" what had already been agreed.

Boris Johnson has faced a double defeat in the Commons after MPs turned down his motion for a general election.
Earlier, MPs backed a bill aimed at blocking a no-deal Brexit if the PM hadn't agreed a plan with the EU ahead of the 31 October deadline.
Mr Johnson said the bill "scuppered" negotiations and the only way forward now was an election.
But Labour leader Jeremy Corbyn accused the PM of "playing a disingenuous game" to force a no-deal Brexit.
He said his party would back an election after the bill had been passed, but not before.
Both the SNP and the Liberal Democrats also criticised the prime minister's motion as a plot to make sure the UK left the EU without a deal.
But supporters of Mr Johnson hit back at opposition members who had been calling for a general election for two years.
Mr Johnson wanted MPs to agree to an early general election on 15 October, saying the bill - which forces him to ask for an extension to the Brexit deadline if no deal had been agreed - left him unable to negotiate a deal.
He needed two thirds of all MPs to vote in favour under the Fixed Term Parliaments Act, but the result only saw 298 vote for the motion and 56 against - 136 short of the number he needed.
Labour sources told the BBC the party abstained on the vote, although three MPs appeared to have voted for it and 28 against.
The SNP also abstained.
The bill to block no deal passed all its stages in the Commons in one day, with the support of most opposition parties and 21 Tory rebels, as they tried to push it through ahead of Parliament being suspended next week.
It will now go to the Lords for approval.
Peers are debating a business motion on how to move forward with the bill - but pro-Brexit peers have laid down over 100 amendments to derail its progress.
Speaking after the vote, the PM attacked Mr Corbyn, claiming he was "the first leader of the opposition in the democratic history of our country to refuse the invitation to an election".
He said he "urged [Mr Corbyn's] colleagues to reflect on the unsustainability of this position overnight and in the course of the next few days."
Earlier, the Labour leader said Mr Johnson's offer of an election was "a bit like an offer of an apple to Snow White from the Wicked Queen... offering the poison of a no deal".
He added: "Let this bill [to block a no deal] pass and gain Royal Assent, then we will back an election so we do not crash out."
One senior MP told the BBC's political editor Laura Kuenssberg that Mr Corbyn had said he would not allow Mr Johnson to have an election before 31 October.
The leader of the SNP in Westminster, Ian Blackford, said the debate about an early election was only going ahead because the PM had lost the vote against the bill.
He added: "[Mr Johnson] must accept the will of this House, accept the bill that Parliament has passed, accept your duty as prime minister and go to the European Council on 17 October and negotiate the extension you have been instructed to deliver."
Leader of the Liberal Democrats, Jo Swinson, praised the cross-party work on the bill as "putting the national interest first", but condemned Mr Johnson's reaction.
"I am intrigued that as a result of this vote... the prime minister's response is this somehow messes up his plan," she added.
"If he is seriously saying the extent of his plan was to try to bully the EU and only get a good deal by threatening [to] leave without a deal... it is not very well thought through."
But Tory MP Nigel Evans criticised the opposition, telling the Commons: "They have been given an opportunity [for an election] and they are running scared - not just from the prime minister, not just from a general election, but from the people of this country who in 2016 said they wanted to leave the EU."
Earlier, shadow Brexit secretary Sir Keir Starmer told Labour MPs the leadership would not back an election until a Brexit delay had been agreed with the EU - making the 15 October proposal impossible.
But the First Minister of Scotland and leader of the SNP, Nicola Sturgeon, tweeted that the opposition parties must "seek to force [an] election" after the bill becomes law but before Parliament is suspended.
She added: "It's starting to feel like Labour doesn't want an election at all and leaving this PM in place knowing he'll try every trick in book to get what he wants would be irresponsible."
The bill says the prime minister will have until 19 October to either pass a deal in Parliament or get MPs to approve a no-deal Brexit.
Once this deadline has passed, he will have to request an extension to the UK's departure date to 31 January 2020 - and, unusually, the bill actually includes the wording of the letter he would have to write.
If the EU responds by proposing a different date, the PM will have two days to accept that proposal. During that time, MPs - not the government - will have the opportunity to reject the EU's date.
The bill also requires ministers to report to the House of Commons over the next few months. potentially providing more opportunities to take control of the timetable.
Be aware though, this could all change over the next few days because MPs and peers have the power to pass amendments to any law.
Meanwhile, the fallout from No 10's decision to withdraw the party whip from 21 Tory rebels who backed the bill to block no deal has continued to face criticism from others in the party.
A group of around 80 Conservatives have written to the prime minister, calling on him to re-instate the whip to the "principled, hard-working and dedicated" MPs.
In a statement on behalf of the "One Nation Caucus", former minister and Tory MP Damian Green said: "Removing the whip from valued colleagues who have served their country and party with distinction damages our hope of winning the next general election."

Prime Minister Boris Johnson has taken the step of writing to all of the MPs who sit in the House of Commons, outlining his plans to ask for a suspension of Parliament in the first half of September. The move will limit the number of parliamentary days available for opponents of a no-deal Brexit to try to block that possibility.
Dear colleague,
I hope that you had an enjoyable and productive summer recess, with the opportunity for some rest ahead of the return of the House.
I wanted to take this opportunity to update you on the Government's plans for its business in Parliament.
As you know, for some time parliamentary business has been sparse.
The current session has lasted more than 340 days and needs to be brought to a close - in almost 400 years only the 2010-12 session comes close, at 250 days.
Bills have been introduced, which, while worthy in their own right, have at times seemed more about filling time in both the Commons and the Lords, while key Brexit legislation has been held back to ensure it could still be considered for carry-over into a second session.
This cannot continue.
I therefore intend to bring forward a new bold and ambitious domestic legislative agenda for the renewal of our country after Brexit.
There will be a significant Brexit legislative programme to get through but that should be no excuse for a lack of ambition!
We will help the NHS, fight violent crime, invest in infrastructure and science and cut the cost of living.
This morning I spoke to Her Majesty The Queen to request an end to the current parliamentary session in the second sitting week in September, before commencing the second session of this Parliament with a Queen's speech on Monday 14 October.
A central feature of the legislative programme will be the Government's number one legislative priority, if a new deal is forthcoming at EU Council, to introduce a Withdrawal Agreement Bill and move at pace to secure its passage before 31 October.
I fully recognise that the debate on the Queen's Speech will be an opportunity for Members of Parliament to express their view on this Government's legislative agenda and its approach to, and the result of, the European Council on 17-18 October.
It is right that you should have the chance to do so, in a clear and unambiguous manner.
I also believe it is vitally important that the key votes associated with the Queen's Speech and any deal with the EU fall at a time when parliamentarians are best placed to judge the Government's programme.
Parliament will have the opportunity to debate the Government's overall programme, and approach to Brexit, in the run up to EU Council, and then vote on this on 21 and 22 October, once we know the outcome of the Council.
Should I succeed in agreeing a deal with the EU, Parliament will then have the opportunity to pass the Bill required for ratification of the deal ahead of 31 October.
Finally, I want to reiterate to colleagues that these weeks leading up to the European Council on 17/18 October are vitally important for the sake of my negotiations with the EU.
Member States are watching what Parliament does with great interest and it is only by showing unity and resolve that we stand a chance of securing a new deal that can be passed by Parliament.
In the meantime, the Government will take the responsible approach of continuing its preparations for leaving the EU, with or without a deal.
The Leader of the Commons will update the House in the normal fashion with regard to business for the final week.
For now, I can confirm that on Monday 9 September both Houses will debate the motions on the first reports relating to the Northern Ireland (Executive Formation etc) Act 2019 (NIEFA).
Following these debates we will begin preparation to end the Parliamentary session ahead of a Queen's Speech.
The Business Managers in both Houses will shortly engage with their opposite numbers, and MPs more widely, on plans for passing a deal should one be forthcoming.
Decisions will also need to be taken about carrying over some of the bills currently before the House, and we will look to work constructively with the Opposition on this front.
If agreement cannot be reached we will look to reintroduce the bills in the next session, and details on this will be set out in the Queen's Speech.
As always my door is open to all colleagues should you wish to discuss this or any other matter.
Yours sincerely,
Boris Johnson

These are the decisions of a prime minister in a hurry.
One who is aware that he's up against the clock.
One who has to pull off - within a few months - what his predecessor could not manage over years.
The team surrounding Boris Johnson has been put together with one goal in mind - to help him keep the promise he's made, to see the country leave the European Union in good time.
Number 10 believes it shows strength of purpose - a new administration determined and willing to take decisions after years of drift and disappointment.
Brexit believers have the top roles. But it is not a cabinet made up purely of the most burning Eurosceptics.
Most of those around the table backed Theresa May's ill-fated deal, so they weren't part of the last stand. They are, in the main, pragmatists not purists - and with prominent former Remainers in there too.
It is perhaps a discernible step to the right - a team that could ready itself to fight a different kind of election, maybe soon, although that's not the intention.
Don't doubt though the scale of the change - one senior Tory described the wholesale clear out as a warped takeover. Another named the new cabinet a Rocky Horror Show.
It's a set of decisions put together to prioritise the task at hand, not to soothe nerves in those who doubt the new prime minister.
But the approach is vintage Johnson - delivered in haste, easy to revile, but a bold statement of intent that's impossible to ignore.

Boris Johnson has delivered his first speech in Downing Street after becoming the UK's new prime minister.
You can read the full text of his speech below.
Good afternoon.
I have just been to see Her Majesty the Queen who has invited me to form a government and I have accepted.
I pay tribute to the fortitude and patience of my predecessor and her deep sense of public service.
But in spite of all her efforts, it has become clear that there are pessimists at home and abroad who think that after three years of indecision, that this country has become a prisoner to the old arguments of 2016 and that in this home of democracy we are incapable of honouring a basic democratic mandate.
And so I am standing before you today to tell you, the British people, that those critics are wrong.
The doubters, the doomsters, the gloomsters - they are going to get it wrong again.
The people who bet against Britain are going to lose their shirts, because we are going to restore trust in our democracy and we are going to fulfil the repeated promises of Parliament to the people and come out of the EU on October 31, no ifs or buts.
And we will do a new deal, a better deal that will maximise the opportunities of Brexit while allowing us to develop a new and exciting partnership with the rest of Europe, based on free trade and mutual support.
I have every confidence that in 99 days' time we will have cracked it. But you know what - we aren't going to wait 99 days, because the British people have had enough of waiting.
The time has come to act, to take decisions, to give strong leadership and to change this country for the better.
And though the Queen has just honoured me with this extraordinary office of state my job is to serve you, the people.
Because if there is one point we politicians need to remember, it is that the people are our bosses.
My job is to make your streets safer - and we are going to begin with another 20,000 police on the streets and we start recruiting forthwith.
My job is to make sure you don't have to wait 3 weeks to see your GP - and we start work this week, with 20 new hospital upgrades, and ensuring that money for the NHS really does get to the front line.
My job is to protect you or your parents or grandparents from the fear of having to sell your home to pay for the costs of care.
And so I am announcing now - on the steps of Downing Street - that we will fix the crisis in social care once and for all with a clear plan we have prepared to give every older person the dignity and security they deserve.
My job is to make sure your kids get a superb education, wherever they are in the country - and that's why we have already announced that we are going to level up per pupil funding in primary and secondary schools.
And that is the work that begins immediately behind that black door.
And though I am today building a great team of men and women, I will take personal responsibility for the change I want to see.
Never mind the backstop - the buck stops here.
And I will tell you something else about my job. It is to be prime minister of the whole United Kingdom.
And that means uniting our country, answering at last the plea of the forgotten people and the left-behind towns by physically and literally renewing the ties that bind us together.
So that with safer streets and better education and fantastic new road and rail infrastructure and full fibre broadband we level up across Britain with higher wages, and a higher living wage, and higher productivity.
We close the opportunity gap, giving millions of young people the chance to own their own homes and giving business the confidence to invest across the UK.
Because it is time we unleashed the productive power not just of London and the South East, but of every corner of England, Scotland, Wales and Northern Ireland.
The awesome foursome that are incarnated in that red, white, and blue flag - who together are so much more than the sum of their parts, and whose brand and political personality is admired and even loved around the world.
For our inventiveness, for our humour, for our universities, our scientists, our armed forces, our diplomacy for the equalities on which we insist - whether race or gender or LGBT or the right of every girl in the world to 12 years of quality education - and for the values we stand for around the world
Everyone knows the values that flag represents.
It stands for freedom and free speech and habeas corpus and the rule of law, and above all it stands for democracy.
And that is why we will come out of the EU on October 31.
Because in the end, Brexit was a fundamental decision by the British people that they wanted their laws made by people that they can elect and they can remove from office.
And we must now respect that decision, and create a new partnership with our European friends -  as warm and as close and as affectionate as possible.
And the first step is to repeat unequivocally our guarantee to the 3.2 million EU nationals now living and working among us, and I say directly to you - thank you for your contribution to our society.
Thank you for your patience, and I can assure you that under this government you will get the absolute certainty of the rights to live and remain.
And next I say to our friends in Ireland, and in Brussels and around the EU: I am convinced that we can do a deal without checks at the Irish border, because we refuse under any circumstances to have such checks and yet without that anti-democratic backstop.
And it is of course vital at the same time that we prepare for the remote possibility that Brussels refuses any further to negotiate, and we are forced to come out with no deal, not because we want that outcome - of course not - but because it is only common sense to prepare.
And let me stress that there is a vital sense in which those preparations cannot be wasted, and that is because under any circumstances we will need to get ready at some point in the near future to come out of the EU customs union and out of regulatory control, fully determined at last to take advantage of Brexit.
Because that is the course on which this country is now set.
With high hearts and growing confidence, we will now accelerate the work of getting ready.
And the ports will be ready and the banks will be ready, and the factories will be ready, and business will be ready, and the hospitals will be ready, and our amazing food and farming sector will be ready and waiting to continue selling ever more, not just here but around the world.
And don't forget that in the event of a no deal outcome, we will have the extra lubrication of the £39 billion, and whatever deal we do we will prepare this autumn for an economic package to boost British business and to lengthen this country's lead as the number one destination in this continent for overseas investment.
And to all those who continue to prophesy disaster, I say yes - there will be difficulties, though I believe that with energy and application they will be far less serious than some have claimed.
But if there is one thing that has really sapped the confidence of business over the last three years, it is not the decisions we have taken - it is our refusal to take decisions.
And to all those who say we cannot be ready, I say do not underestimate this country.
Do not underestimate our powers of organisation and our determination, because we know the enormous strengths of this economy in life sciences, in tech, in academia, in music, the arts, culture, financial services.
It is here in Britain that we are using gene therapy, for the first time, to treat the most common form of blindness.
Here in Britain that we are leading the world in the battery technology that will help cut CO2 and tackle climate change and produce green jobs for the next generation.
And as we prepare for a post-Brexit future, it is time we looked not at the risks but at the opportunities that are upon us.
So let us begin work now to create free ports that will drive growth and thousands of high-skilled jobs in left-behind areas.
Let's start now to liberate the UK's extraordinary bioscience sector from anti-genetic modification rules, and let's develop the blight-resistant crops that will feed the world.
Let's get going now on our own position navigation and timing satellite and earth observation systems - UK assets orbiting in space, with all the long term strategic and commercial benefits for this country.
Let's change the tax rules to provide extra incentives to invest in capital and research.
And let's promote the welfare of animals that has always been so close to the hearts of the British people.
And yes, let's start now on those free trade deals - because it is free trade that has done more than anything else to lift billions out of poverty.
All this and more we can do now and only now, at this extraordinary moment in our history.
And after three years of unfounded self-doubt, it is time to change the record.
To recover our natural and historic role as an enterprising, outward-looking and truly global Britain, generous in temper and engaged with the world.
No one in the last few centuries has succeeded in betting against the pluck and nerve and ambition of this country.
They will not succeed today.
We in this government will work flat out to give this country the leadership it deserves, and that work begins now.
Thank you very much.

Boris Johnson has said the row over the border in Northern Ireland is being used to frustrate Brexit.
The foreign secretary insisted there were "very good solutions" to avoid the need for a hard border.
There is a stand-off on the issue with the EU publishing a legal draft of its Brexit withdrawal agreement.
An option for Northern Ireland to follow EU rules to avoid a "hard border" - if an alternative arrangement is not agreed - has sparked a row.
The Democratic Unionist Party, which offers vital support in key votes to the Tory government, says details of the draft treaty have "fundamentally breached" an agreement reached in Brussels late last year.
Conservative Brexiteers say it is "completely unacceptable" and would effectively annex Northern Ireland.
The European Union's chief negotiator, Michel Barnier, unveiling the draft agreement, described this Northern Ireland border option as a "backstop" if no other proposals are found. And a former EU commissioner said it was down to the UK to come up with a solution, warning that "at a high pace we are heading to the cliff edge".
BBC assistant political editor Norman Smith said it was shaping up to become "the big Brexit bust-up" with both sides of the argument refusing to budge.
Mr Johnson faced criticisism on Tuesday for suggesting in a BBC interview the issue of the border could be managed as easily as London's congestion charging zone.
Speaking to Sky News on Wednesday, he said: "What is going on at the moment is that the issue of the Northern Irish border is being used quite a lot politically to try and keep the UK in the customs union - effectively the single market - so we cannot really leave the EU. That is what is going on."
"If the EU or Dublin believes the UK government will be signing up to a border in the Irish Sea, they are deluded," said senior DUP member Sir Jeffrey Donaldson.
Mr Donaldson argued the draft divorce treaty would also undermine the constitutional status of Northern Ireland in the Belfast Agreement.
That 1998 treaty - also known as the Good Friday Agreement - between the British and Irish governments and most political parties in Northern Ireland decided how the region would be governed and brought an end to 30 years of sectarian conflict.
Former Brexit minister David Jones told BBC Radio 4's Today programme the EU was proposing that Northern Ireland stay in the customs union, and subject to the jurisdiction of the European Court of Justice.
"That effectively amounts to an annexure of Northern Ireland by the European Union," he said, adding: "I think that it would be pretty catastrophic and I think that the European Union in actually proposing this is behaving wholly irresponsibly."
But former EU trade commissioner Karel de Gucht said: "If you have another solution then please come up with it."
All of the UK's proposals so far have been "mutually incompatible", he added.
And Irish Prime Minister Leo Varadkar told RTE that in order to avoid the backstop being triggered,  "it is up to the UK to bring proposals to the table to make that possible".
He added: "It's not OK for people, whether pro-Brexit politicians in Britain, people or parties in Northern Ireland, to just say 'no' now."
The draft document aims to encapsulate - in legally binding language - agreements already reached on Ireland, citizens' rights and the UK's so-called "divorce bill".
It mandates that during the Brexit transition, which it says should last only until the end of 2020, the UK must continue to comply with all existing EU legislation. It would however lose all voting rights and decision-making power, including on any rules adopted by the 27 remaining member states.
EU negotiator Michel Barnier has said the document will not contain any surprises because it translates the political pledges made by both sides in the talks so far.
"The clock is ticking; time is short," Mr Barnier said at a news conference on Tuesday. "I am concerned."
Theresa May wants trade to be frictionless across the Irish border after Brexit.
But there is plenty of political friction as every potential solution seems to bring a new problem.
In a leaked letter designed to demonstrate that there would be no need for new infrastructure between Northern Ireland and the Republic, Boris Johnson used a potentially toxic phrase: "even IF there is a hard border".
This allowed critics to suggest that a regime of border checks which would be anathema to republicans, nationalists and the Irish government was being contemplated.
Downing Street swiftly reiterated its commitment to no hard border.
But one of the solutions - indeed, the most detailed option - being put forward by the EU would keep Northern Ireland aligned with EU regulations.
The DUP's Jeffrey Donaldson has said the government cannot sign up to what would in effect be a border in the Irish Sea.
And with rebellions threatened by some of her own backbenchers, Mrs May is likely to need the DUP's MPs to deliver the Brexit she's promising.
The prime minister's office has categorically dismissed any prospect of a return to a "hard border" in Ireland as a consequence of Brexit.
The statement on Tuesday evening followed the leak of a letter to the prime minister from Mr Johnson, in which he appeared to contemplate the possibility of future customs border checks, after the UK, including Northern Ireland leaves the EU customs union.
The leaked letter, obtained by Sky News, quoted Mr Johnson telling the prime minister the return of a hard border on the island of Ireland would continue to leave 95% of traffic to pass unchecked.
Following the letter's emergence, Labour called for Mr Johnson - one of the leading Brexiteers in the cabinet - to be dismissed "before he can do any more damage".
A spokesman for Mr Johnson said the letter was "designed to outline how a highly facilitated border would work and help to make a successful Brexit".
"It shows how we could manage a border without infrastructure or related checks and controls while protecting UK, Northern Ireland, Irish and EU interests."

Boris Johnson says there should be "no doubt" the only alternative to the Brexit proposals he will put to Brussels later is no-deal.
Addressing his party conference in Manchester, the PM said his plan would be a "compromise by the UK", but he hoped the EU would "understand that and compromise in their turn".
The European Commission said they will "examine [the proposals] objectively".
The Irish PM said he had not seen the plans but was "not encouraged".
Leo Varadker told the Irish Parliament: "What we are hearing is not encouraging and would not be the basis for agreement."
The UK is set to leave the EU on 31 October.
The government has insisted it will not negotiate a further delay beyond the Halloween deadline, saying this would be unnecessary and costly for the UK.
However, under the terms of a law passed by Parliament last month, the PM faces having to request another extension unless MPs back the terms of withdrawal by 19 October - two days after a summit of European leaders.
The European Commission's President Jean-Claude Juncker and Mr Johnson will speak on the phone later, and the two sides' negotiating teams will also meet.
In his speech, Mr Johnson said no-deal was not an outcome the government was seeking, but "it is an outcome for which we are ready".
On the eve of his speech, Mr Johnson told a conference fringe meeting, hosted by the DUP, that he hoped to reach a deal with the EU over the course of "the next few days".
The issue of the Irish border - and how to keep it free from border checks when it becomes the frontier between the UK and the EU - has been a key sticking point in Brexit negotiations.
Mr Johnson has said the solution reached by the EU and Theresa May, the backstop, is "anti-democratic" and "inconsistent with the sovereignty of the UK", claiming it offered no means for the UK to unilaterally exit and no say for the people of Northern Ireland over the rules that would apply there.
The PM used his speech to confirm parts of his offer to the EU.
He said that "under no circumstances" would there be checks at or near the border in Northern Ireland and the proposals would respect the peace process and the Good Friday agreement.
It included promising "a process of renewable democratic consent" for the Stormont Assembly on its relationship with the EU going forward.
He also referred to the use of technological solutions to ensure there was no hard border on the island of Ireland.
He said he did not want a deal to be out of reach "because of what is essentially a technical discussion of the exact nature of future customs checks when that technology is improving the whole time".
Mr Johnson also said he would "protect the existing regulatory arrangements for farmers and other businesses on both sides of the border".
He added: "At the same time we will allow the UK - whole and entire - to withdraw from the EU, with control of our own trade policy from the start."
The PM said this would "protect the union".
Echoing the main slogan of the conference, Mr Johnson said: "Let's get Brexit done on 31 October…to answer the cry of those 17.4 million who voted for Brexit [and] for those millions who may have voted Remain, but are first and foremost democrats and accept the result of the referendum."
He said the Tories were "not an anti-European party" and the UK is "not an anti-European country".
The PM added: "We love Europe. We are European.
"But after 45 years of really dramatic constitutional change, we must have a new relationship with the EU."
This speech was hugely important for Boris Johnson's Brexit deal.
Be in no doubt that amongst those listening most closely, most intently, will be leaders in other European capitals, trying to gauge whether Mr Johnson is serious about a Brexit deal or whether he is paving the way for no-deal and looking to blame the EU.
This was actually a rather surprising speech because there was none of the aggressive, combative language that we had been expecting - none of the in your face, take it or leave it final offer that we were told would form the guts of his argument.
Instead, it seemed Mr Johnson went out of his way to adopt a rather more emollient approach, saying how much he loved Europe, how the Tory Party wasn't an anti-European party and how Britain wasn't an anti-European country.
What that meant was that Mr Johnson didn't endeavour to bring the house down in the conference hall. He didn't go for the easy Brussels bashing, and for the wider viewers in this country, there were no brand new policy announcements.
You sense Mr Johnson has calculated for the next few hours and days that the really crucial audience in terms of his premiership, and for his future, is not here in Manchester - it's in capitals around the EU.
Before Mr Johnson's speech, a European Commission spokeswoman said they would examine the proposals objectively, adding: "We will listen carefully to the UK."
She said the EU wanted to agree a deal with the UK, saying "an orderly withdrawal is far more preferable than a 'no-deal' scenario".
But the spokeswoman also reminded the UK of its "well-known criteria",  saying: "In order for there to be a deal, we must have a legally operational solution that meets all the objectives of the backstop.
"[That means] preventing a hard border, preserving North-South cooperation and the all-island economy, and protecting the EU's Single Market and Ireland's place in it."
Leo Varadker said he would work until the last moment to secure an agreement, but he added: "We will not do so at any cost, and we are ready for no-deal if that's what the British decide to do."
The BBC's Europe editor, Katya Adler said the bloc wanted to do a deal and needed to be seen to try.
But she added it was "fundamentally misunderstanding the EU" if the prime minister believed the other 26 EU leaders will turn round to Ireland and say they have to accept the proposals just they want to have a deal.
There were huge rounds of applause for Mr Johnson from within the conference hall, showing support from his party.
After the speech, one member said the PM was "exactly what we need", while another said she had been "inspired", adding: "We are so fed up with nothing happening, but we feel like something will happen now because we think he will deliver."
Leaving the hall, Tory MP Mims Davies described her leader as "bombastic Boris", saying: "That [speech] was a message to the country, a message to our party and a message to the EU - we are ready to get on with this."
But the PM's plan has been branded as "extreme" and "doomed to failure" by the SNP's Westminster leader, Ian Blackford, who said his strategy was leading towards a no-deal.
Shadow chancellor John McDonnell said the prime minister's speech was "absolute bluster" and he described it as a "cynical manipulation to get a no-deal".
Mr McDonnell also that any Brexit deal or no-deal should be put to the people to make the final decision.
The director general of the CBI, Dame Carolyn Fairbairn, praised the PM's "optimistic vision for the UK".
But she said his plan "relies on a good Brexit deal".
"The UK is at a crossroads," she said. "[And] the no-deal turning ends in a very different place: a swamp that will slow the UK's every step for years to come."
The PM also used the opportunity to criticise Parliament, saying it "refuses to deliver Brexit, refuses to do anything constructive and refuses to have an election".
He said: "I am afraid that after three and a half years people are beginning to feel that they are being taken for fools."
Mr Johnson said the Tories were "the party of the NHS" because of their belief in capitalism, adding: "We understand the vital symmetry at the heart of the modern British economy between a dynamic enterprise culture and great public services precisely because we are the party of capitalism."
He praised London as its former mayor, but pledged to "unlock talent in every corner of the UK", and ensure safety with his existing policies of 20,000 additional police officers and tackling county lines gangs.
And he repeated more policy announcements from the conference on infrastructure, education, law and order.
Mr Johnson concluded: "Let's get on with sensible moderate one nation but tax-cutting Tory government and, figuratively if not literally, let us send Jeremy Corbyn into orbit where he belongs.
"Let's get Brexit done [and] let's bring our country together."
Mr Johnson's conference speech clashed with Prime Minister's Questions.
Normally the Commons goes into recess for the Tory conference, but MPs voted against this amid the bitter fallout from the government's unlawful prorogation of Parliament.
Foreign Secretary Dominic Raab deputised for the prime minister, facing the shadow home secretary Diane Abbott over the despatch box.
He told MPs the government will present its written Brexit proposals to them later.
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Boris Johnson has told the BBC that Britain should reject any EU demands for a £50bn "exit bill" and follow the example of former PM Margaret Thatcher.
It has been reported that EU negotiator Michel Barnier has said the UK must continue to pay into the EU until 2020.
Mr Johnson said it was "not reasonable" for the UK to "continue to make vast budget payments" once it left the EU.
He cited Mrs Thatcher's success at the 1984 Fontainebleau Summit, when she threatened to halt payments to the EU.
Laura Kuenssberg: Thatcher to inspire UK 'Brexit bill' talks?
Poland fails to stop Tusk EU re-election
"I think we have illustrious precedent in this matter, and you will doubtless recall the 1984 Fontainebleau Summit in which Mrs Thatcher said she wanted her money back, and I think that is exactly what we will get," he told BBC political editor Laura Kuenssberg in BBC Two's Brexit: Britain's Biggest Deal.
"It is not reasonable, I don't think, for the UK having left the EU to continue to make vast budget payments, I think everybody understands that and that's the reality."
The UK won the rebate in 1984, after then prime minister Margaret Thatcher threatened to halt payments to the EU budget.
At the time the UK was then the third poorest member of the Community but was on course to become the biggest net contributor to the EU budget.
Asked about Mr Johnson's comments, Mrs May said "there was only ever one Margaret Thatcher" and insisted the British people did not vote for Brexit to keep paying "huge sums" into the EU budget.
The Daily Telegraph has reported that Mr Barnier raised the idea that the UK may have to pay 60bn euros (£52bn) to cover the UK's share of outstanding pension liabilities, loan guarantees and spending on UK-based projects until 2020 - even if it leaves the EU by 2019.
Irish premier Enda Kenny suggested he may back demands for the UK to pay a "divorce bill" when it leaves the EU, telling reporters at the summit on Thursday: "When you sign on for a contract, you commit yourself to participation.
"And obviously the extent of that level of money will be determined. Mr Barnier is the lead negotiator for the European Union and obviously Britain will have a say.
"But that no more than any other problem will have to be faced, it will have to be dealt with and it will be dealt with."
Meanwhile, in London, ministers have cleared time for MPs to vote on reversing Lords Brexit bill amendments.
Commons Leader David Lidington announced that the bill will be debated by MPs on Monday, 13 March.
Ministers hope to overturn peers' calls for a "meaningful" parliamentary vote on the final terms of the UK's withdrawal from the EU.
They also want to reverse a Lords defeat on the issue of guaranteeing the rights of EU citizens in the UK.
At the summit, the 28 EU leaders discussed migration, security and economic growth, but the meeting began with a vote backing former Polish prime minister Donald Tusk remaining European Council president - a move opposed by Poland's government.
Polish Prime Minister Beata Szydlo had accused predecessor Mr Tusk of interfering in the country's domestic affairs.
The president is elected by the European Council by a qualified majority, which means that no single country can veto it.
At the summit, Mrs May called for more action to counter "Russian disinformation" and "raise the visibility" of Western commitment in the western Balkans, where Moscow faces allegations of helping to plot a coup attempt in Montenegro.
She is leaving the summit on Thursday.
The other 27 leaders are expected to use Friday's informal meeting to discuss the next summit in Rome on 25 March, which will celebrate the EU's 60th anniversary.
A government source suggested Mrs May, who plans to trigger Article 50 this month - the mechanism that kick-starts the UK's departure from the EU - will not be attending the Rome summit.

It is fair to say it has been a confusing day, but what do we actually know tonight?
No 10 have prepared a proposal for a "Temporary Customs Arrangement", where the UK would retain close ties to the EU for an indeterminate period after the end of the transition period - past 2020 - in case none of their hoped for customs fixes come to pass.
They believed they had the support of senior ministers to publish it on Thursday, even without explicit and detailed discussions of the written paper itself in the inner Brexit cabinet, let alone the full gathering of senior ministers.
It became clear, however, and rather surprisingly to the outside observer, that the man in government who is meant to be in charge of the Brexit process was not completely on-board.
So the brakes have been slammed on publishing the paper until meetings and discussions between senior ministers tomorrow.
No 10 is trying to find a way of satisfying Brexit Secretary David Davis, who is not just concerned about the lack of time limit in this particular proposal, but also Downing Street's refusal so far to publish his hoped for Brexit blueprint before the end of this month, and a lack of decision about the government's preferred long term option on customs.
Again, therefore, No 10 has had to row back because it either didn't fully understand the level of unhappiness inside cabinet, or because they were aware of it but believed they could push on regardless - because the imperative of cracking on with the Brexit process is more important than political sensitivities at home.
Brexiteers on the Tory benches would have been likely to erupt at the current proposal with no end date. So, if David Davis' desires can be as one source suggested "managed" tomorrow, his fury may have avoided a wider revolt.
But Theresa May's internal critics believe this is yet another product of her reluctance to face down those in her party who want to impose their vision on her achingly slow journey to compromise.
Again, the government stumbles when trying to resolve its own internal contradictions, before being able to confront the EU 27.
This latest saga may yet be solved in the next 24 hours. But it is not impossible to imagine that it may not, with a potential, if perhaps not yet likely, resignation of David Davis.
And again, the irony is that the UK is tying itself in knots over a position that the EU is likely to reject.

The Liberal Democrats have won the Brecon and Radnorshire by-election, leaving new PM Boris Johnson with a working majority in Parliament of one.
Jane Dodds overturned an 8,038 majority to beat Conservative Chris Davies by 1,425 votes.
Mr Davies stood again after being unseated by a petition following his conviction for a false expenses claim.
It was the first electoral test for Mr Johnson just eight days after becoming prime minister.
It was also the quickest by-election defeat for any new prime minister since World War Two.
Now, with the thinnest majority, he will have to rely heavily on the support of his own MPs and his confidence-and-supply partners the DUP to get any legislation passed in key votes.
It was a bad night for Labour, whose vote share dropped by 12.4% as it was beaten into fourth place by the Brexit Party.
The result means the Lib Dems now have 13 MPs.
Ms Dodds, who is the Welsh Liberal Democrat leader, said: "My very first act as your new MP when I get to Westminster will be to find Mr Boris Johnson, wherever he's hiding, and tell him to stop playing with the future of our community and rule out a no-deal Brexit."
Mr Davies congratulated Ms Dodds saying "I wish her well for the future" and paid tribute to his family saying they had "a difficult time over the past few months".
The turnout was 59.6%, down from 74.6% at the general election, but it is the highest for a by-election since Winchester in 1997.
Neither Plaid Cymru nor the Greens fielded candidates, to try to maximise the Remain vote.
Tory party chairman James Cleverly told BBC Radio 4's Today programme it was a "very close result in a by-election in which the Lib Dems were expected to romp home comfortably".
In a message to Conservative MPs concerned about the government's Brexit policy he said the new prime minister had received a "clear mandate from parliamentarians" and an "even more thumping victory in the leadership election".
"I do think it's incumbent on all Conservatives to support the prime minister in what has been a long-standing Conservative policy," he said.
But recently-elected Liberal Democrat leader Jo Swinson said: "Boris Johnson's shrinking majority makes it clear that he has no mandate to crash us out of the EU."
She denied the party had "played" the system by striking a deal with Plaid Cymru and the Greens.
"I want to have a different voting system but we're working within the system that we have," she said.
Celebrating victory later on Friday morning with party activists, Ms Swinson said the Lib Dems were "winning again" and she would "fight to keep our country in the European Union".
Ms Dodds, 55, lives in the neighbouring mid Wales constituency of Montgomeryshire and is a child-protection social worker.
The Lib Dems have held the rural seat for all but nine of the last 34 years and lost at the 2015 general election.
Plaid Cymru leader Adam Price said the "spirit of co-operation" between the pro-Remain parties had led to Ms Dodds's election, as he called for another EU referendum.
"But if the prime minister is intent on a general election, he should know that Plaid Cymru and the other pro-Remain parties are committed to cooperating so that we beat Brexit once and for all," he said.
Wales Green Party leader Anthony Slaughter said its decision to withdraw from the by-election was "absolutely vindicated" by the result.
"The people of Brecon and Radnorshire have taken the opportunity to cut Boris Johnson's majority in Westminster to a highly unstable one, reducing further the risk of a disastrous crash-out Brexit," he said.
Labour leader Jeremy Corbyn called the result "disappointing".
He added: "The Liberal Democrats won it after doing a deal with Plaid Cymru and the Greens.
"I think that a lot of voters were determined to get rid of the Conservative, and they voted accordingly. So we were squeezed, but it's a place we have not held for a very long time. The area has changed a bit."
Prof Laura McAllister, from Cardiff University's Wales Governance Centre, said the result should not be read as a "resounding victory" for Remain.
She pointed out that the three Brexit-supporting parties had 2-3,000 votes more than the Remain alliance.
But she added: "There are always nuanced undercurrents to this. The reality is Brexit isn't the only issue people were voting on.
"People were probably voting on rural and local issues. We can never categorically say this was about Brexit."
Sir John Curtice, professor of politics at Strathclyde University, said the Conservatives were enjoying a "Boris bounce" and the result was encouraging for the party despite the loss.
But he added: "In an early general election, at the moment at least, the Conservatives would be at risk of losing."
He said the Lib Dems could pick up 40 or 50 seats, which would make winning a large overall majority "rather more difficult for the Conservatives".
By Jonathan Blake, BBC political correspondent
As the ballots were counted, the candidates looked on - neither the Tories nor the Liberal Democrats dared to claim victory or concede defeat.
One thing was certain, the result when it came would be close.
But a win is a win and the Lib Dems will shout this from the rooftops as proof they can cut through with an anti-Brexit message.
The Remain alliance proved to be a winning formula, as Plaid Cymru and the Green Party stood aside to give the Lib Dems a clear run against the Tories.
If the Brexit Party hadn't been standing, the Conservatives might have clinched it.
Labour will look hard at its disastrous result and wonder what might have been with a clearer message on Brexit.
And for the Tories, the people of Brecon and Radnorshire have delivered an unwelcome verdict on their former MP and the new prime minister.
Boris Johnson's hands were already tied in parliament and the ropes around his wrists have just been pulled a little tighter.
At one stage Labour feared it might lose its deposit and blamed voters switching tactically to the Lib Dems.
A Welsh Labour spokesman said: "We always knew this was going to be a difficult night for us, but we're proud of our positive campaign in Brecon and Radnorshire."
"One thing is clear - voters have rejected Boris Johnson and his divisive, out-of-touch UK Tory government."
Political analyst Prof Roger Awan-Scully, from Cardiff University, said: "Labour need to look very closely at this result. Everything points to not just tactical voting for the Lib Dems but also dissatisfaction with Jeremy Corbyn and [First Minister] Mark Drakeford."
The Brexit Party's Des Parkinson, a retired police chief superintendent, who finished third, said: "If you look at the actual total of the vote, the Brexiteers won.
"It shows where the votes are but the prime minister has to deliver a clear Brexit... if he doesn't, then his government is in dire trouble."
The Monster Raving Loony Party pushed the UKIP candidate into sixth place.
Voters have also given their thoughts on the result.
Farmer Trevor Walters voted for Mr Davies and said the Tories might have won, had the Brexit Party not stood, but called the speculation over a Brexit no-deal fallout "scaremongering".
He added: "We're not going to be left in the lurch. I don't think for one second that'll happen. Something will be done to sweeten the blow of all that and get us engaged with a proper trade deal."
Independent book shop owner Emma Corfield-Walters, who backed the Lib Dems, said: "None of us know what's going to happen in the future.
"I think we're all entirely confused on the Brexit issue and I think this result shows us."

Hospitals are likely to experience delays to cancer testing and treatment regardless of the result of next week's Brexit vote, BBC Newsnight has learned.
The Royal College of Radiologists has told doctors to prepare for possible delays for some drugs used to detect cancer if there is a no-deal Brexit.
It says clinicians should reduce their workload in the days after 29 March, when the UK is due to leave the EU.
The government said it had "robust" plans for however the UK leaves the EU.
MPs will vote on Prime Minister Theresa May's Brexit withdrawal agreement by 12 March.
If Parliament does not vote in favour of her deal and there is no extension of Article 50 - the two-year process for leaving the EU - the UK will leave with no withdrawal agreement, known as a no-deal Brexit.
The five-page guidance to doctors from the Royal College of Radiologists (RCR), seen by Newsnight, warns that some radiopharmaceutical suppliers "anticipate there may be some delay to their delivery times".
It advises clinicians to: "Keep [your] workload lighter for the first week following a no-deal Brexit, in order to see more clearly what the impact is likely to be."
It adds: "In the weeks leading up to Brexit you should consider how to prioritise requests based on clinical need, should supplies be compromised."
The guidance refers to the radioisotopes commonly used in the diagnosis and treatment of some cancers.
These cannot be stockpiled in advance because of the rapid decay of their radioactivity and "a one-day delay to delivery would reduce available activity by approximately 20%", according to the guidance from the RCR.
A spokesman for the RCR told Newsnight the organisation now believed it was "inevitable" that uncertainty over Brexit would cause delays to some cancer tests and treatments.
Dr Richard Graham said: "Of course, now there will inevitably be delays to treatment as a result of the Brexit process because we need to start booking our lists for the post-Brexit date.
"We will need to book clinics less heavily so that we've got more wriggle room if we don't have the radioisotopes in order to diagnose and treat the patients."
Dr Graham said the RCR had met with the Department of Health and Social Care several months ago "when they were very optimistic that there would be a deal" and that the guidance would not be necessary.
"But unfortunately now it looks like no deal really is a tangible possibility, so it's vital that we get this guidance out now so patients treatment and diagnosis is disrupted at the bare minimum."
Dr Graham said it would have been "much easier" for medics if they had known that a no-deal Brexit was not going to happen.
"But of course we understand that might be a negotiating strategy to get the best deal for the country.
"Putting patients' health at risk for the sake of getting a good Brexit deal is a difficult priority to balance."
The Department of Health and Social Care has asked radiopharmaceutical suppliers to use air freight in the event of a no-deal Brexit, as that is expected to cause road disruption.
But the guidance states that "some companies feel their plans will ensure no delays but others anticipate there may be some delay to their delivery times".
And on one specific type of treatment, known as radionuclide therapy, it states that "only one supplier has been confident it will be able to deliver therapy doses on particular required days".
The radiologists' warning that it is now too late to escape some disruption - even if Mrs May secures majority Parliamentary support for her withdrawal agreement - follows similar statements from other sectors.
UK-based financial firms have already had to establish offices elsewhere in the EU in case they suddenly find themselves unable to service European clients from 29 March.
And surveys show that stockpiling by manufacturing firms is at the highest level on record due to the fear of a no-deal Brexit.
A Department of Health and Social Care spokesperson said: "Leaving the EU with a deal remains the government's top priority.
"As a responsible government we have robust contingency plans in place so patients can continue to have access to medicines, including medical radioisotopes, whatever the EU Exit outcome.
"We have worked with the pharmaceutical industry to ensure that planes are contracted to bring in medical radioisotopes under the appropriate specialist conditions and suppliers are working closely with the NHS to minimise any potential impact of changes to delivery times."

European Council President Donald Tusk has said he will appeal to EU leaders "to be open to a long extension" of the Brexit deadline, if the UK needs to rethink its strategy and get consensus.
His intervention came as UK MPs voted to seek a delay of the 29 March deadline to leave the EU.
EU leaders meet in Brussels on 21 March and they would have the final say.
Prime Minister Theresa May has said that if her Brexit deal is not approved a longer extension may be necessary.
After two resounding defeats in the House of Commons, she will make another attempt by 20 March to push through her Withdrawal Agreement with the EU.
MPs backed a government motion on Thursday to extend the two-year deadline to 30 June if the Mrs May's deal is passed next week, while noting that a longer extension would be necessary if it is rejected.
All 27 other EU nations would have to agree to an extension, and Mr Tusk, who is the bloc's summit chairman, will hold talks with several leaders ahead of next week's Brussels meeting.
While European Commission President Jean-Claude Juncker has insisted that any postponement "should be complete before the European elections" at the end of May, Mr Tusk made clear a longer delay was on the cards.
While he did not specify the length of the delay, officials suggested it would have to be at least a year if the UK prime minister's deal was rejected a third time.
Mr Tusk said earlier this year that the EU's hearts were still open to the UK if it changed its mind about Brexit. He provoked an angry reaction from pro-Brexit supporters when he said there was a "special place in hell" for those who had promoted Brexit "without even a sketch of a plan of how to carry it out safely".
So at this crucial point, what do Europe's leaders think about extending Article 50, the two-year treaty provision that the UK invoked on 29 March 2017?
Jenny Hill in Berlin
"A lot of the trust is gone." Among business and political figures in Berlin, there's growing frustration, even anger, at developments in Britain.
Nevertheless, Germany is likely to do all it can to help facilitate the orderly Brexit which Angela Merkel insists is still possible.
The German chancellor won't be drawn publicly on whether she would support an extension to Article 50, but it's widely accepted here that she and her government would be willing do so.
There are those who believe that support should be conditional upon Britain's ability to outline its reasons and expectations before such an extension is granted. And there are significant concerns about the impact of a longer extension upon the EU elections but Germany's interests lie in avoiding a no-deal Brexit – and the damage that could wreak on the German economy.
Its government will do what it can to achieve that aim.
Dr Norbert Roettgen, who chairs the foreign affairs committee, urged Britain and the EU to take their time.
"Everything is hectic, hysterical, unclear. Let's slow down and try to get a clear head," he said. "The world will not end if we all take time for a breather, focus on important points."
"If we try to rush a result now it will definitely go wrong."
Hugh Schofield in Paris
As a "frontline" country which effectively shares a border with the UK – thanks to the Channel Tunnel –  France has more to fear than most from a no-deal Brexit.
Yet when it comes to granting London more time, President Emmanuel Macron is expected to insist on conditions.
He will not approve an extension if it simply means putting off the pain.
A "technical" extension of a few weeks would be an easy matter, according to Elvire Fabry of the Jacques Delors Institute in Paris.
Even if the House of Commons had approved Theresa May's plan on Tuesday, such an extension would probably have been inevitable, and automatically approved at the EU summit next week.
"But a longer extension poses all sorts of problems. No-one is comfortable with the idea of the UK taking part in the EU elections in May. It would be a most unwelcome distraction," Ms Fabry said.
"So for a longer extension there would have to be a very clear and precise objective written in - for example new elections in the UK or a new referendum."
She said that Brussels "was pretty favourable" to the idea – but in the last few days things had changed.
"No-one over here is saying, 'let's just get it over with and have a No Deal.' That fatigue seems to be gaining ground in the UK, but not in Europe."
"Here everyone is exhausted and impatient – but we feel there is nothing much more we can do. It's the Brits who have to sort this out among themselves."
Adam Easton in Warsaw
"The British people have decided the UK should leave, it should be concluded. Otherwise it would be a humiliation."
That's how one MEP from the governing party, Ryszard Legutko, put it, adding: "A second referendum or too long an extension would also be a humiliation".
Top officials are a little more gentle.
Poland's foreign minister, Jacek Czaputowicz, has said the UK may need a little more time.
"We are watching what is happening in the UK - the votes, there are certain expectations about how they will end. Maybe we will need to… extend this period a bit, maybe a little more time is needed for reflection," he told reporters in the Polish parliament.
"From our point of view a no-deal Brexit is the worst solution."
For Warsaw, securing the rights of the estimated one million Poles living in the UK has always been and remains the number one priority, and the two governments are in "constant contact".
But Poland is hoping for a deal and a smooth transition period. That's because the UK is Poland's third-largest sales market.
Anna Holligan in Rotterdam
Dutch Foreign Minister Stef Blok has told the BBC his country would look "with benevolence" at any request to extend Article 50. But "without a clear goal an extension won't solve anything", he warned.
The mantra "hope for the best, prepare for the worst" underpins the Dutch approach, and Mr Blok was at an event showcasing the government's preparations for a no-deal exit.
"I'm looking forward to any solution that will solve the problem, but that has to come from London now."
The Dutch never wanted the UK to leave the EU but respected its choice. Now they view any possible extension a little like tearing off a sticking plaster. Ideally it should be done rapidly to get the pain over with.
"We're living in the reality Brexit has dealt us", says foreign trade minister Sigrid Kaag, gesturing towards a stream of trucks trundling on to a ferry bound for the UK port of Felixstowe.
"(The Netherlands) is your natural gateway to Europe. With a stable government. We're not sitting idle, we're not panicking, we're getting ready for any eventuality."
James Reynolds in Rome
Italy would support an extension of Article 50 on two conditions:
Italy believes that the UK government is genuine when it says it doesn't want No Deal, a senior Italian official, who asked not to be named, told the BBC.
But, at the same time, Italy is not shy about preparing for No Deal. In the next few days, the government is hoping to pass a package of laws aimed at addressing its priorities : citizens' rights, financial stability, help for businesses.
Next week, the Rome government expects to roll out a series of information sessions in ports around the country to explain how No Deal would work.

The international border between Northern Ireland and the Republic of Ireland is about 310 miles long with, depending on how many tracks you include, as many as 275 crossing points.
In reality, the entire border is a crossing point because, apart from road signs changing from miles per hour to kilometres per hour, there is no physical infrastructure to see.
The concern is that all that could change when the UK leaves the European Union, and Ireland stays as an EU member state.
Part of the concern is political. The 1998 Good Friday Agreement, the basic building block of peace in Northern Ireland, removed security checkpoints from the border and helped make it all but invisible. Customs checks could undermine much of that progress.
Like many peace deals, the Good Friday Agreement is a masterpiece of creative ambiguity, allowing different people to take different things from different parts of the text.
Shared membership of the European Union made that much easier to achieve. Ireland wants a clear written commitment that the agreement will be respected in all its parts.
The other concern of course is economic. The economies of Northern Ireland and the Republic are completely interconnected. Huge amounts of goods and services cross the border every day without checks of any kind.
Brexit negotiators are currently looking through more than 140 areas of north-south co-operation, involving everything from the single electricity market to environmental protection.
It is also estimated that at least 30,000 people cross the border every day for work. The movement of people is governed by the Common Travel Area between the UK and Ireland, which predates the EU.
Both sides are determined that the Common Travel Area will remain in place, but that in itself doesn't resolve the challenge of a hard border re-emerging.
Because the UK has announced that it is leaving the EU single market and the customs union. That immediately turns the internal border in Ireland into an external border for the single market and the customs union - with all the potential checks that implies.
At the moment, all rules and regulations, north and south, are exactly the same - on food safety, on animal welfare… you name it.
Again, it's a relationship based in large part on agreements covered by joint membership of the EU. As soon as that changes, border checks may have to begin again.
That's why the Irish government wants a written guarantee from the UK that Northern Ireland will continue to follow EU rules - so goods can continue to move freely across the border.
"It seems essential to us," said the Irish Foreign Minister Simon Coveney earlier this month, "that there is no emergence of regulatory divergence from the rules of the internal market or the customs unions which are necessary for meaningful north-south co-operation, or an all-Ireland economy that is consistent with the Good Friday Agreement."
In other words, both Ireland and the rest of the EU are suggesting that Northern Ireland should stay within the customs union and the single market.
Yes. It would - in effect - push the customs border out into the Irish Sea... an internal customs border, if you like, between Northern Ireland and Great Britain.
Would that be acceptable to the UK government, or to its Unionist political allies in Northern Ireland, the DUP? In a word, no.
"We respect the European Union desire to protect the legal order of the single market and customs union," the UK's Brexit Secretary David Davis said in Brussels recently.
"But that cannot come at a cost to the constitutional and economic integrity of the United Kingdom."
If it did that then, under World Trade Organization rules, it would have to do the same for the rest of the world. The UK economy would be swamped with cheap imports.
The EU would impose checks anyway which might allow the UK government to shift the blame on to Brussels. But that would be a pretty futile gesture.
If it was easy, it would already have been done.
The EU argues that the UK's red lines on Ireland - no border on the one hand, and UK exit from the single market and the customs union on the other - are fundamentally incompatible.
The British government has spoken of technological fixes such as pre-screening of goods, and trusted trader schemes.
The EU says such things could speed up border transit, but it would be nowhere near enough to avoid the return of some border checks.
Alternatively, Irish officials argue that there are already cases of rules and regulations being different in Northern Ireland than in the rest of the UK, and they point to other examples such as Hong Kong in China where there are different regulatory arrangements within sovereign states.
Intense negotiations are taking place to try to come up with a solution that would ensure a) no divergence of regulations in key areas; and b) the creation of some form of customs partnership on the island of Ireland, which doesn't threaten the constitutional order of the UK.
But if a fix emerges that seems to turn Northern Ireland into a back door route into the single market, then other EU countries will cry foul.
So even if all parties agree in the next two weeks that "sufficient progress" on Ireland has been made, there will be a long way to go before any kind of lasting solution emerges.
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The pavement cafes and bars were packed last Sunday as Brussels basked in an unseasonably warm weekend.
Among the drinkers were diplomats from the EU member states who had been kept in the dark ever since negotiators from the European Commission and UK had entered an intense and secret period of talks, jokingly known as "the tunnel".
"You can have a couple but not too many," advised one official close to the talks, hinting that movement was imminent.
After more than a week of radio silence, the rest of the European machine believed that a provisional agreement on the Brexit divorce treaty was just hours away.
The aperitifs were abandoned after the UK announced that Brexit Secretary Dominic Raab would be in Brussels for face-to-face talks with his opposite number Michel Barnier.
Ambassadors from the 27 other member states were told to prepare for an early-evening briefing. Diplomats said the mood music was good.
But British sources warned the situation was not as positive as it appeared and there were still serious outstanding issues, particularly with the so-called "backstop" - the back-up plan to avoid to a hard border on the island of Ireland that could see Northern Ireland staying in the EU's customs union.
A tweet from Michel Barnier changed the mood.
Negotiations would be "paused" until EU leaders gathered for a Brexit-themed dinner on Wednesday. Both sides sounded seriously depressed.
The Politico website then claimed that officials had reached a deal at a technical level that "collapsed" when the Brexit Secretary became involved.
It made British civil servants desperate to prove that the prime minister's European adviser, Olly Robbins, had not drafted his own deal that had angered his political masters.
By Monday morning, Downing Street had coined a new phrase to explain the stumbling block: the "backstop to the backstop".
It was a way to rebrand the EU's insistence that Northern Ireland should stay in the customs union in the event no other solutions were found to avoid the need to reintroduce a border.
Theresa May reminded the House of Commons of her alternative of a UK-wide customs arrangement with the EU, which had been tabled in the summer as a "Temporary Customs Arrangement".
Previously described as a "bridge" between the post-Brexit transition (or "implementation") phase, it was now "our backstop".
Brussels noted with approval that the prime minister had talked about a process for deciding when it should come to an end instead of a date - a formula that was "event-driven" rather than time-specific.
It was also much closer to the phrase agreed with the EU that any backstop would be in place "unless and until" another solution is found.
And it would be legal for the EU to commit to during the Brexit process whereas a permanent customs solution was not, confirmed a European official who quoted the European treaties.
Meanwhile, it was suggested privately that the two sides had found a way to address the other half of the Irish border problem: keeping Northern Ireland aligned with the rules of the single market needed to avoid checks on the Irish border, but not necessarily avoiding them between Northern Ireland and Great Britain.
Theresa May also suggested that more progress had been made than people realised in the talks on the future relationship, including on financial services.
The day before EU leaders were to meet, Michel Barnier travelled to Luxembourg to update European affairs ministers.
He made a passing reference to the idea of extending the post-Brexit transition phase but gave few details. The UK seemed relaxed about the story despite the fact it would dominate the rest of the week.
Then came the first of a three-day marathon of seven separate summits in Brussels.
Every EU leader spoke from the same script on Brexit: there was no decisive progress but they wanted to carry on talking.
"Do no harm and avoid anyone feeling offended when they leave," was the slogan.
Theresa May was given a 15-minute slot in which to make her case. A diplomat said she spoke so quickly it was as if she had a plane to catch.
The other leaders dined on pan-fried mushrooms, turbot and sorbet without the prime minister.
Inside the room Irish Taoiseach Leo Varadkar brandished a copy of an Irish newspaper, with a front page devoted to a murder during the Troubles to demonstrate Ireland's emotional case alongside its economic one.
Outside the room, European officials stuck to their concept of a Northern Ireland-only backstop but said they were prepared to "camouflage" it to make it as palatable as possible to the British.
One compared it to a child being distracted from a bowl of spinach by filling the table with more appetising food.
A potential extension of the transition period was part of this effort.
It was a possibility that Mrs May was "cautiously" open to, an official confirmed. The president of the European Parliament, Antonio Tajani, said the same.
Dinner ended with the leaders saying there would be no planning for a Brexit summit in November, but leaving the door open to one if the negotiations made progress.
Talk of no deal - often perceived as a hostile act - was kept to a minimum.
And officials reassured British journalists that a late-night drink featuring Angela Merkel, Emmanuel Macron and others - but not Theresa May - was a celebration of the Luxembourgish election results rather than a "screw you" to the UK.
"You guys are so paranoid," said an ambassador.
Disaster had been avoided but the transition proposal had created a domestic political nightmare for the prime minister.
Downing Street was now trying to play the proposal down: "Just an idea…. it'll never be used."
Their focus was getting a legally binding reference to a UK-wide customs arrangement into the paperwork that would comprise the final Brexit deal, and they were exasperated that media coverage of the summit was dominated by the transition issue.
Then there was confusion when European Council President Donald Tusk said during a press conference that the 27 leaders had not discussed the concept, and yet European Commission President Jean-Claude Juncker said it would "probably" end up happening.
"Chaotic and un-coordinated" is the way one European diplomat described the Brexit component of the summit.
He blamed too little planning, a lack of precision from the European Commission and not enough co-ordination among the member states.
As the EU's multiple summits came to an end, Theresa May's fellow leaders suggested that the negotiations could not restart until the prime minister acknowledged that the Withdrawal Agreement had to contain an option for the backstop that might apply to Northern Ireland but not the rest of the UK.
The UK would also have to accept that its aspiration of truly friction-less trade could only be achieved by staying in the EU's customs union and sticking to the rules of the single market.
In other words: there are some tasty goodies on offer, but Britain will only be invited back to the table when it is prepared to eat its greens.
Listen to Adam Fleming and the rest of the BBC's Brexitcast team for the lowdown from Brussels and Westminster

Theresa May faces a battle to get a key piece of Brexit legislation through Parliament, opponents have warned.
Shadow Brexit Secretary Sir Keir Starmer said it was "highly likely" Labour would seek to amend the Repeal Bill, which aims to convert EU legislation into British law.
The SNP, Lib Dems and Green MP Caroline Lucas will also press for changes.
The bill, described by the PM as an "essential step" to EU withdrawal - was the centrepiece of the Queen's Speech.
It will repeal the 1972 European Communities Act, which took Britain into the EU and meant that European law took precedence over laws passed in the British parliament.
It starts its Parliamentary journey next week but it is not likely be debated on the floor of the Commons until the autumn, with some predicting fireworks as MPs on all sides bid to change Mrs May's approach to Brexit in a series of votes.
Last month, 49 Labour MPs defied party leader Jeremy Corbyn by backing a Queen's Speech amendment calling for Britain to stay in the single market and customs union after Brexit.
Conservative backbenchers opposed to what they regard as a "hard Brexit" are also reported to be plotting to force changes to the Repeal Bill.
Labour rebels are understood to be planning to join forces with Tory rebels, the Lib Dems and the SNP to force changes to the Repeal Bill, and future pieces of Brexit legislation.
The Labour leadership backs an exit from the single market but wants to protect EU safeguards on employment rights and the environment - and is concerned these could be scrapped or watered down by the Repeal Bill.
Speaking to BBC Radio 4's Today programme, Sir Keir said the Labour leadership was likely to table amendments that would seek to curb the power of government ministers to amend or scrap EU laws without MPs' scrutiny.
He said: "I think it's highly likely we will want to table that push amendment dealing with the scope of power given to the executive but also to concentrate on issues such as enforcement of rights and protections."
Green Party co-leader Caroline Lucas told the programme she was also preparing to amend the Bill, while the SNP's Stephen Gethins said his party "had a responsibility" to work with others over the terms.
Former Brexit minister David Jones, who lost his frontbench role in the post-election reshuffle, said Labour should back the government over the Bill after promising to deliver Brexit in its manifesto.
Pressed on the scale of the challenge, he told the Today programme: "Clearly there is huge pressure, though, having said that, I have no doubt that we will be able to do it."
Of 27 Bills and draft Bills in the Queen's Speech, eight were devoted to leaving the EU.
In addition to the Repeal Bill, there were separate pieces of legislation on  on customs, trade, immigration, fisheries, agriculture, nuclear safeguards and the international sanctions regime.

David Davis, who has been leading UK negotiations to leave the EU, has quit his role as Brexit Secretary
He told the BBC that he was no longer the best person to deliver the PM's Brexit plan - agreed by the cabinet on Friday - as he did not "believe" in it.
He said the "career-ending" decision was a personal one but he felt the UK was "giving away too much and too easily" to the EU in the negotiations.
Mrs May said she did not agree but thanked him for his work.
The resignation is a blow to Mrs May as she seeks to win over Eurosceptic MPs to her proposed Brexit vision, which would form the basis of the UK's position in on-going talks with the EU.
Dominic Raab, who campaigned for Leave during the UK's 2016 EU referendum, has been promoted from housing minister to take over from Mr Davis.
The UK is due to leave the European Union on 29 March 2019, but the two sides have yet to agree how trade will work between the UK and the EU afterwards.
There have been differences within the Conservative Party over how far the UK should prioritise the economy by compromising on issues such as leaving the remit of the European Court of Justice and ending free movement of people.
Mrs May's Conservative Party only has a majority in Parliament with the support in key votes of the 10 MPs from Northern Ireland's Democratic Unionist Party, so any split raises questions about whether her plan could survive a Commons vote - and has also led to renewed questions about whether she will face a challenge to her position.
In a sign of how delicately positioned the numbers are on Brexit strategy it has emerged that the government has taken the unusual step of arranging a briefing for opposition Labour MPs on the detail of the Brexit plan agreed on Friday.
In his resignation letter, Mr Davis told Mrs May that "the current trend of policy and tactics" was making it "look less and less likely" that the UK would leave the customs union and single market.
He said he was "unpersuaded" that the government's negotiating approach "will not just lead to further demands for concessions" from Brussels.
Mr Davis, who was appointed Brexit Secretary in 2016, said: "The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one."
In her reply, Mrs May said: "I do not agree with your characterisation of the policy we agreed at cabinet on Friday."
She said she was "sorry" he was leaving but would "like to thank you warmly for everything you have done... to shape our departure from the EU".
Mr Davis told BBC Radio 4's Today programme that he had objected to Theresa May's plan at the Chequers meeting, telling cabinet colleagues at the outset that he was "the odd man out".
He said it was "not tenable" for him to stay in post and try to persuade Tory MPs to back the policy when he did not think it was "workable".
"The best person to do this is someone who really believes in it, not me."
He said he feared the EU would seek to further water down the UK's plans and his resignation would make it easier for the UK to resist attempts to extract further concessions.
Mr Davis told BBC political editor Laura Kuenssberg that he had been compromising for two years and that the latest plan was "a compromise too far".
But Mr Davis insisted he continued to back Theresa May, saying that if he "wanted to bring her down", the time would have been after she failed to win last year's general election outright.
A leadership contest now would be "the wrong thing to do", adding: "I won't throw my hat into the ring."
Eurosceptic MP Steve Baker has also resigned. He played a leading role in the Brexit campaign in the run up to the 2016 referendum. He was promoted to the Department for Exiting the EU as a parliamentary under-secretary in June last year.
Conservative MP Peter Bone hailed Mr Davis's resignation as a "principled and brave decision", adding: "The PM's proposals for a Brexit in name only are not acceptable."
Labour Party chairman Ian Lavery said: "This is absolute chaos and Theresa May has no authority left."
By BBC political editor Laura Kuenssberg
After many months of rumours that he would pull the plug, David Davis has actually quit as Brexit Secretary.
His unhappiness in government has been no secret for some time, but after the prime minister's Chequers agreement with cabinet ministers to pursue closer ties with the EU than he desired, he found his position untenable.
After a visit to Downing Street on Sunday he concluded that he had no choice but to walk.
The move, while not completely surprising, throws doubt on to how secure the government's Brexit strategy is.
Read Laura's full blog here
Mrs May is due to address MPs on Monday afternoon and is expected to tell MPs that the strategy agreed by the cabinet at Chequers on Friday is the "right Brexit" for Britain.
Brexiteer MP Jacob Rees-Mogg said it would be "very difficult" for Mrs May's plans to win the backing of MPs without Mr Davis.
He told BBC 5 Live: "These proposals will have to come to the House of Commons in legislation and the question is 'will they command support from Conservative MPs?'
"And I think without David Davis there, without his imprimatur, it will be very difficult for them to get the support of Conservative MPs and therefore the prime minister would be well advised to reconsider them."
BBC political editor Laura Kuenssberg said she understands Mr Davis was "furious" after a meeting at No 10 earlier on Sunday and "concluded he could not stay in post".
The resignation came as people awaited the verdicts of senior figures from the Brexit side of the 2016 referendum.  There has yet been no on the record comment from Foreign Secretary Boris Johnson, while Environment Secretary Michael Gove told the BBC on Sunday he was urging Tory MPs to support Mrs May.
One of the leading pro-Remain Conservative MPs Anna Soubry did not refer directly to Mr Davis's resignation, but tweeted it was "not the time for egos, grandstanding and blind ideology".
The director-general of the CBI, Carolyn Fairbairn, said the resignation was "a blow", adding that business had welcomed the agreement of ministers on Friday.
Meanwhile, some Remain-supporting politicians said the resignation was evidence of the need for a second referendum.
Lord Adonis, a prominent backer of a second vote, tweeted: "People's Vote to put Brexit out of its misery a big step closer after DD's resignation. Now the Brexiteers holding Mrs May hostage are falling out, there isn't a majority for any withdrawal treaty in Parliament."
The Liberal Democrats called on people to sign a petition for a vote on the proposed deal, adding: "The resignation of David Davis is yet more evidence of the chaos of this Tory Brexit. You deserve the final say".
Nigel Farage congratulated Mr Davis for quitting and called for Mrs May to be replaced as prime minister, accusing her of being "duplicitous" and claiming her response "shows she is controlled by the civil service".

MPs are trying to influence the Brexit process in a number of ways, as Theresa May continues her bid to get the EU to change the deal.
The prime minister has asked MPs to approve a motion on Thursday simply acknowledging that process is ongoing and restating their support for the approach.
Several MPs tabled amendments setting out alternative plans and Commons Speaker John Bercow has selected three to be put to a Commons vote.
Even if they won the backing of a majority of MPs, the proposals would not be binding on the government. However, they could put pressure on Mrs May to change course.
She has adopted proposals from two successful backbench amendments tabled in January.
One asked her to seek alternatives to the "backstop", which aims to prevent the return of customs checkpoints on the Irish border in the event that no trade deal has come into force. The other rejected leaving the EU without a formal exit deal.
The selected proposals are below. Use our guide to Brexit jargon or follow the links for further explanation.
Required the government to either give MPs a vote on the withdrawal agreement and political declaration on future UK-EU relations by 27 February, or make a statement saying there is no longer an agreement in principle with Brussels and so allow MPs to vote on - and amend - its planned next steps.
Labour Leader Jeremy Corbyn's amendment was defeated by 322 votes to 306, giving the government a majority of 16.
Sought to postpone the Brexit date by at least three months.
This had the backing of Liberal Democrats, as well as the SNP contingent.
However, most Labour MPs abstained and so the amendment was defeated by 93 votes to 315.
Instructed the government to publish within seven days "the most recent official briefing document relating to business and trade on the implications of a no-deal Brexit presented to cabinet".
This had the backing of some mostly Remain-supporting Labour and Conservative backbenchers.
But Ms Soubry withdrew the amendment after Brexit Minister Chris Heaton-Harris indicated that Cabinet Office Minister David Lidington would meet her and would be publishing the relevant information.
Ms Soubry welcomed the move but said she reserved the right to lay the amendment again at end of February if the government did not publish the documents.

Prime Minister Theresa May has laughed off journalists' questions about going to war with Spain following the Gibraltar Brexit row.
Mrs May said her approach to negotiations was "definitely jaw jaw".
On Sunday ex-Tory leader Lord Howard said the PM would defend Gibraltar in the same way as Margaret Thatcher defended the Falklands in the 1982 war.
Spain's foreign minister said his government was "surprised by the tone of comments coming out of Britain".
"It seems someone is losing their cool," Alfonso Dastis told a conference in Madrid.
The current row was sparked by draft Brexit negotiating guidelines published by the EU last Friday saying any decisions affecting Gibraltar would be run past Spain.
The guidelines said: "After the United Kingdom leaves the Union, no agreement between the EU and the United Kingdom may apply to the territory of Gibraltar without the agreement between the Kingdom of Spain and the United Kingdom."
Speaking to reporters on a flight to Jordan, Mrs May was asked if - borrowing from a phase used by Winston Churchill - Britain's approach should be described as "jaw jaw, not war war".
"It's definitely jaw jaw," replied the PM, who laughed when asked to rule out a war with Spain.
"What we are doing, with all EU countries in the EU is sitting down and talking to them," she said.
"We're going to be talking to them about getting the best possible deal for the UK and for those countries - Spain included."
Mrs May said British policy on Gibraltar had not, and would not, change.
Gibraltar: key facts
Gibraltar's chief minister Fabian Picardo said: "Gibraltar is not a bargaining chip in these negotiations. Gibraltar belongs to the Gibraltarians and we want to stay British."
Mr Picardo urged European Council President Donald Tusk to remove the reference to Gibraltar.
"Mr Tusk, who has been given to using the analogies of the divorce and divorce petition, is behaving like a cuckolded husband who is taking it out on the children," he said.
The EU's guidelines followed a letter from Mrs May formally triggering Brexit talks, which did not mention Gibraltar directly.
Lord Howard raised the spectre of military action, saying that 35 years ago, "another woman prime minister sent a taskforce halfway across the world to protect another small group of British people against another Spanish-speaking country.
"And I'm absolutely clear that our current woman prime minister will show the same resolve in relation to Gibraltar as her predecessor did."
After Argentina invaded the Falklands in 1982, Margaret Thatcher sent a task force to reclaim the islands, in the South Atlantic.
An estimated 655 Argentine and 255 British servicemen lost their lives in the fighting that followed.
Former Labour foreign secretary Jack Straw, whose 2002 referendum asking Gibraltarians if they wanted Britain to share sovereignty with Spain was rejected by 99% to 1%, dismissed the threat of military action as "frankly absurd and reeks of 19th century jingoism", adding that Britain leaving the EU would result in "all sorts of problems" popping up.
"For the Spanish, Gibraltar is an affront to their sense of national identity and their sense of sovereignty - it's a bit like having a part of Dover owned by Spain," he told BBC Radio 4's Today programme.
Mr Straw said while Britain was in the EU "we held equal cards with Spain", but once it left, the situation would be reversed, with the 27 EU nations "holding the cards".
Lib Dem leader Tim Farron said of Lord Howard's comments: "In only a few days the Conservative right are turning long-term allies into potential enemies."
But Brexit Secretary David Davis, in Spain for meetings with members of its government, said Lord Howard was expressing the "resolve" of the UK in supporting the sovereignty of Gibraltar. He made it clear any talk of Falklands style taskforces "wasn't going to happen".
Former Labour minister Lord Foulkes used House of Lords' question time to ask why Gibraltar had not been mentioned in Mrs May's letter to the EU last week, which triggered the start of Brexit negotiations.
Foreign Office Minister Baroness Anelay of St John's replied, saying the government took the matter "so seriously" it did not want to mention just one aspect of the negotiations in a letter that set out general principles which all applied to Gibraltar.
Spain has long contested Britain's 300 year-rule of Gibraltar, which has a population of about 30,000.

Lots of things can be true at the same time, even though they seem to contradict each other. It happens a lot in politics as, if you read my ramblings here often, you'll know I've said before.
This time, lots of seemingly contradicting strands are combining to create a situation that is potentially dangerous for Theresa May, and not very helpful for the UK's case in the Brexit negotiations.
Yes, it is true that a powerful group of Brexiteers believe that they have been told by No 10, that any effort to water down the government's position on the Customs Union would be treated as a vote of confidence, to bring rebel Remainers to heel.
This is in the context not of this week's vote, which would not have any power to force a change of heart, but a vote that will have that authority next month.
It is also true that those potential rebel Remainers believe they have been assured by the government that they would NOT turn a vote on the customs union into a vote of confidence. They think they can try to shift Theresa May's position without collapsing the government, indeed they say the chatter about a confidence vote is a 'ruse' by the Brexiteers.
Downing Street says publicly that no such decision has been made. It's not surprising that in uncharted territory they don't want to be bound to one position now over a vote that's not for another month.
But it is also true that No 10 cannot sustain a situation where the two opposing sides in the Tory party who are in perma-campaign mode, are continually told the opposite. It is not possible to drive left and right at the same time.
It is also true that the government's public position has been clear for ages - to leave the customs union and pursue two separate potential models, the 'hybrid' and the 'max fac' . If you want to But it is also true that some Cabinet ministers believe that only the second option is remotely viable. Even in No 10 senior figures accept that they are nowhere near being able to prove to the EU that the hybrid model would work.
Even the Brexit Secretary himself, David Davis, questioned its credibility almost as soon as it was published, saying it was "blue sky thinking". Many months on, at least in public, there doesn't seem to be much evidence that would change his or other Brexiteer ministers' views.
That's why there are whispers, as on the front of today's Times, that he and others might try to force the PM to ditch it.
It's also the case that there has not been enough progress towards sorting out the Irish border question. Whether the UK should call the EU's bluff as some Brexiteers suggest, or accept what others see as inevitable and change position, is a different question. For as long as the question is open, the border question is a proxy for the whole debate about the world after Brexit.
Should we mirror the existing arrangements we have to minimise disruption, or go for a more radical break?
The most important truth is that with a divided party and no majority, it's massively difficult for Theresa May to settle that question.
Her survival so far has hinged on only inching forward, but pressure is building through the proxy of the arguments about the customs union, to take a bolder next step.

Is the DUP about to do a 180 and support checks in the Irish Sea as part of a Brexit deal?
Political u-turns aren't unheard of, after all.
But in this case, it seems a good way off.
Newspaper reports that the DUP has privately shifted its red lines on the backstop were quickly - and publicly - panned by senior party figures.
But is that the full story?
It's important to set out what the DUP has said it will accept, and how its tone has changed in recent days, causing a whiff of hope about a potential deal.
The party has always made protecting the union its main priority, delivering Brexit second - and in the early stages of the negotiations insisted there could be no deal that allowed any splits to develop between Northern Ireland and Great Britain.
It had, however, said it could accept certain regulatory differences that didn't damage trade with Great Britain or undermine the Union.
The Northern Ireland Assembly would also need to have oversight of the process.
While continuing to oppose the backstop, the party has softened its language, saying it would be open to all-island "arrangements" on food standards and animal health, which could partially remove the need for some checks at the land border.
That would mean Northern Ireland continuing to follow some EU rules and accepting new checks on some goods coming in from Great Britain
They haven't set out precisely what the arrangements could look like - don't expect them to either.
The Times story hinted the DUP could accept EU rules in other areas too - which is perhaps why the party has pushed back so hard.
If the DUP is going to to back anything that even slightly resembles NI only accepting EU rules, they will need to be able to sell it.
Their ideas are being talked about by the prime minister as well.
Boris Johnson has found himself boxed in by Parliament, and by demanding the backstop disappear, he has few options left when it comes to getting a deal by his Halloween deadline.
So is a compromise of sorts coming down the tracks?
There have certainly been warmer words this week from some in Brussels, with Ireland's EU commissioner Phil Hogan saying he believed there is "movement on both sides".
But we still don't know quite how the landing zone for a last-minute deal will look.
Will the DUP and Boris Johnson, despite their protestations, go further than all-island "arrangements" and move towards a Northern Ireland-specific solution?
What will the EU be prepared to sign up to?
If Stormont has the power to refuse to accept new EU regulations on food standards that would fall short of guaranteeing no hard border in the future.
Could Stormont have a consultative role on those EU issues which would apply in Northern Ireland?
Bear in mind that would require Stormont to get back up and running first, but there is a theory that if a deal is reached, there would be a two-year transition period which could allow some breathing space for devolution to be restored in order for Stormont to play its part.
There's also the question of trust: The DUP say they do not believe Boris Johnson will turn his back on them and sign up to anything they disagree with.
Others aren't so sure.
Cynics might say stories in the national press that the DUP is softening are an attempt by someone to bounce the party into accepting something else.
Right now, political tactics are being deployed on all sides.
No-one wants to be seen to budge too much.
Despite what the key players will all say publicly, they know someone will have to give more, and accept more.
Behind the scenes, what is being discussed could be very different - as pressure is applied for an agreement to take shape.
Boris Johnson has said he really wants to leave the EU with a deal on 31 October.
It may now be a question of who can shout louder at him about what that deal should look like, in the seemingly short time that's left.

Boris Johnson has hit the pause button on his Brexit legislation after MPs rejected his plan to get it through the Commons in three days.
MPs backed his Withdrawal Agreement Bill - but minutes later voted against the timetable, leaving it "in limbo".
After the vote, EU Council President Donald Tusk said he would recommend EU leaders backed an extension to the 31 October Brexit deadline.
But a No 10 source said if a delay was granted, the PM would seek an election.
On Saturday, Mr Johnson complied with a law demanding he write to the EU to ask for a three-month extension, but did not sign the letter.
Following the result in the Commons, he said it was Parliament and not the government that had requested an extension.
Mr Johnson said he would reiterate his pledge to EU leaders, telling them it was still his policy to leave by the end of October.
But Commons leader Jacob Rees-Mogg told MPs it was "very hard" to see how the necessary laws could be passed to leave with a deal by the deadline.
A spokesman from the European Commission said: "[The Commission] takes note of tonight's result and expects the UK government to inform us about the next steps."
But Mr Tusk tweeted he would "recommend the EU27 accept the UK request for an extension" in order to "avoid a no-deal Brexit".
The BBC's Europe editor Katya Adler said: "[The] temptation amongst most I speak to tonight in EU circles is to grant the 31 Jan extension."
And the BBC's political editor Laura Kuenssberg said that meant the government's plan to seek an election was "looking likely".
However, an EU source told BBC Brussels reporter Adam Fleming the bloc was considering a "flextension" - an extension with a maximum end date, but the flexibility for the UK to leave early if a deal is ratified.
Following Tuesday's Commons votes, a Downing Street source said Parliament "blew its last chance".
They added: "If Parliament's delay is agreed by Brussels, then the only way the country can move on is with an election."
Labour leader Jeremy Corbyn said Mr Johnson was "the author of his own misfortune".
He told the Commons that MPs had "refused to be bounced into debating a hugely significantly piece of legislation in just two days, with barely any notice or an analysis of the economic impact of this bill".
But Mr Corbyn offered to enter discussions over a "sensible" timetable for the PM's deal to go through Parliament.
The SNP's leader, Ian Blackford, said it was "another humiliating defeat" for the PM, and MPs had "spoken with a very clear voice to tell the PM he is not on".
Liberal Democrat leader Jo Swinson called on Mr Johnson to "end the brinkmanship and replace it with some statesmanship" in order to secure an extension with the EU.
Boris Johnson agreed his new plan with EU leaders last week, but has repeatedly pledged to leave the bloc by the end of October, with or without a deal.
This is despite him having to ask for an extension to Brexit on Saturday after MPs backed an amendment attempting to block a no-deal.
The bill that would turn his plan into law - the Withdrawal Agreement Bill - was published on Monday evening, and he urged MPs to back a three-day timetable to push it through the Commons ahead of the Halloween deadline.
The PM told Parliament if it "decides to delay everything until January or possibly longer", he would seek an election - but he did not say what the government would do if the EU offered a shorter extension.
MPs did approve the bill on its first hurdle through the Commons - called the second reading - by 329 votes to 299.
But in a vote straight after, they rejected the so-called programme motion, in other words the planned timetable to get the bill through Parliament, by 14 votes after a number of MPs criticised the pace of the legislation.
Mr Johnson told the Commons: "I will speak to EU member states about their intentions [but] until they have reached a decision - until we reach a decision, I will say - we will pause this legislation."
In the meantime, however, he said the government would "take the only responsible course and accelerate our preparations for a no deal outcome".
The PM added: "Let me be clear. Our policy remains that we should not delay [and] that we should leave the EU on 31 October."
If an election were to be triggered this week, the earliest it could take place would be Thursday 28 November, as the law requires 25 days between an election being called in Parliament and polling day.
But Mr Johnson cannot force an election himself and would need the backing of Parliament.
MPs had been due to debate the bill over Wednesday and Thursday, but will now return to discussing the contents of the Queen's Speech - which put forward the government's domestic agenda for the new session of Parliament.
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The government's Brexit bill will enable more British judges to depart from previous rulings of the EU's top court, Downing Street says.
The PM's spokesman said the Withdrawal Agreement Bill would expand this power to courts below the Supreme Court.
He added this would ensure judges at lower courts would not be "inadvertently" tied to the rulings "for years to come".
But others warned the move would cause legal uncertainty.
MPs are set for an initial vote on the withdrawal bill on Friday, after the Conservatives won an 80-seat majority at last week's general election.
Previous rulings of the European Court of Justice (ECJ) are set to be incorporated into the case law followed by British courts after Brexit.
The provision is contained in a separate EU withdrawal law passed in June last year under the premiership of Theresa May.
Previously, only the Supreme Court and the High Court of Justiciary in Scotland would be allowed to depart from these rulings.
Prime Minister Boris Johnson's spokesman said enabling lower courts to do the same was an "important change" to ensure they do not face a "legal bottleneck".
"We will take back control of our laws and disentangle ourselves from the EU's legal order just as was promised to the British people," he said.
There is no real detail in the government's pledge - but it marks a potentially really significant development.
It means that UK civil courts below the Supreme Court, for example the Court of Appeal, High Court, county courts, and tribunals such as the Employment Appeal Tribunal could depart from ECJ rulings in areas such as workers' rights.
Take for instance the right to paid holidays. The ECJ has interpreted this right more generously than the UK courts: for example, on the inclusion of overtime in holiday pay, and currently its interpretation binds the UK courts.
Following the 11 month transition period after Brexit, the way is open, for example, for an employer to take a case to one of the UK's lower civil courts and invite a judge to apply a more restrictive interpretation to the right to paid holidays.
This would create plenty of work for lawyers, but it opens a can of worms and could affect many workers.
The government's move was welcomed by former Tory leader Iain Duncan Smith, a leading figure in the pro-Brexit European Research Group.
"This is a critical pledge that puts sovereign rights back in the hands of the UK government and of course the British people," he said.
However, crossbench peer Lord Pannick QC, who acted for businesswoman Gina Millar in two cases against the government over its handling of Brexit, cautioned against the measure.
He told the Times, which first reported on the move, that allowing lower courts to depart from ECJ rulings would "cause very considerable legal uncertainty".
The government is hoping to get its Brexit deal through Parliament in the new year, enabling the UK to leave the EU by the end of January.
If passed, the UK would then follow EU rules during an 11-month transition period due to conclude at the end of December 2020.
MPs in the previous Parliament gave initial backing to the PM's Brexit bill but rejected his plan to fast-track the legislation through Parliament in three days in order to leave the EU by the then Brexit deadline of 31 October.
The government has already said the amended version of the withdrawal bill that will come back before MPs on Friday will include a new clause to rule out any extension to the transition period beyond the end of next year.

The UK has two weeks to clarify key issues or make concessions if progress is to be made in Brexit talks, the bloc's chief negotiator has said.
Michel Barnier was speaking after meeting the Brexit secretary for talks on citizens' rights, the Irish border, and the UK's "divorce bill".
David Davis said it was time for both sides "to work to find solutions".
Before the talks, Theresa May said she wanted the UK's exit date set in law, and warned MPs not to block Brexit.
Speaking at a press conference in Brussels, Mr Barnier suggested Britain would have to clarify its position in the next fortnight on what it would pay to settle its obligations to the EU if the talks were to have achieved "sufficient progress" ahead of December's European Council meeting.
"It is just a matter of settling accounts as in any separation," Mr Barnier said.
Mr Barnier also said both sides had to work towards an "objective interpretation" of Prime Minister Theresa May's pledge that no member of the EU would lose out financially as a result of the Brexit vote.
The Brexit secretary insisted good progress was being made across the board, and that the negotiations had narrowed to a "few outstanding, albeit important, issues".
Mr Davis and Mr Barnier agreed there had been progress on the issue of settled status for EU citizens in the UK after Brexit.
Mr Barnier said the UK had provided "useful clarifications" on guaranteeing rights, although more work needed to be done on some points including rights of families and exporting welfare payments.
For the UK's part, Mr Davis said, the government had "listened carefully" to concerns and that there would be a "streamlined and straightforward" process for EU nationals to obtain settled status.
But Mr Davis rejected a suggestion that Northern Ireland could remain within the European customs union.
He was responding to a European Commission paper, which proposed that Northern Ireland may have to remain a member of the EU's single market or customs union, if a so-called "hard border" with the Irish Republic is to be avoided.
Saying there had been "frank discussions" with Mr Barnier and his negotiators on the issue of the Irish border, Mr Davis insisted there could be "no new border" inside the UK.
"We respect the European Union desire to protect the legal order of the single market and the customs union, but that cannot come at cost to the constitutional and economic integrity of the United Kingdom," Mr Davis told reporters in Brussels.
"We recognise the need for specific solutions for the unique circumstances of Northern Ireland.  But let me be clear - this cannot amount to creating a new border inside our United Kingdom," he added.
Mr Barnier said the "unique situation" on the island of Ireland required "technical and regulatory solutions necessary to prevent a hard border".
By Adam Fleming, BBC Europe correspondent
Michel Barnier usually says at post-negotiation press conferences that the clock is ticking.
He didn't this time: he gave a specific timeframe. He wants the UK to provide more clarity in the next two weeks on its positions on the rights of EU citizens who wish to remain after Brexit, the plans for the Irish border and principles for calculating Britain's financial obligations.
Although the EU doesn't want a precise figure, it wants the UK to clarify what it's willing to pay to live up to the financial commitments made as a member.
On Ireland, both sides have pledged to protect the peace process but the EU has suggested that might require Northern Ireland sticking to European rules on customs and the single market - rules that the rest of Britain might not follow in future. David Davis rejected that.
UK sources agree it looks like they've been set a deadline but they feel it is a logical reading of the EU's timetable, under which their officials have to begin preparations for the next summit of EU leaders in December fairly soon.
Looking ahead to December's EU summit, Mr Davis pledged the UK was "ready and willing" to engage with Brussels "as often and as quickly as needed".
"But we need to see flexibility, imagination and willingness to make progress on both sides if these negotiations are to succeed and we are able to realise our new deep and special partnership," he said.
Friday's update came as Prime Minister Theresa May announced she wanted the date the UK leaves the EU - 29 March 2019 - enshrined in law.
The prime minister said the decision to put the specific time of Brexit "on the front page" of the Brexit bill showed the government was determined to see the process through.
"Let no-one doubt our determination or question our resolve, Brexit is happening," she wrote.
The draft legislation has already passed its second reading, and now faces several attempts to amend it at the next part of its parliamentary journey - the committee stage.
Mrs May said the government would listen to MPs if they had ideas for improving the bill, but warned against attempts to halt the process.
"We will not tolerate attempts from any quarter to use the process of amendments to this bill as a mechanism to try to block the democratic wishes of the British people by attempting to slow down or stop our departure from the European Union."

European Council President Donald Tusk has said a compromise with the UK over Brexit is "still possible", after Theresa May warned she was prepared to walk away from talks.
In a statement, Mr Tusk said he was a "true admirer" of the PM.
But he defended the EU's approach and said it was in fact Mrs May who had been "tough" and "uncompromising".
Mrs May on Friday demanded more respect from Brussels after EU leaders rejected a major part of her Brexit plan.
She had tried to sell her blueprint, which was agreed by ministers at Chequers, to EU countries at a summit in Salzburg, Austria, this week.
But the EU said the new economic partnership she had put forward "will not work" and risked "undermining the single market".
The UK is due to leave the EU on 29 March 2019 - but the two sides are trying to reach a deal by November so it can be ratified in time.
Mr Tusk issued a statement on Friday evening, hours after Mrs May delivered her own speech in Downing Street in which she said the EU's rejection of her plan without offering an alternative was "unacceptable".
Mr Tusk said EU leaders at the summit had treated her proposals with "all seriousness" and said they were a "step in the right direction".
Britain had known about the EU's reservations over the Chequers plan for weeks, he added.
Mr Tusk said: "While understanding the logic of the negotiations, I remain convinced that a compromise, good for all, is still possible.
"I say these words as a close friend of the UK and a true admirer of PM May."
Mrs May's statement dominates many of Saturday's front pages.
The Express calls her speech her "finest hour" and says she was right to demand respect from the EU and the Daily Mail says Mrs May "confronted the arrogance of the EU elite with unyielding, level-headed reason" and describes the EU's behaviour in Salzburg as "shabby".
The Sun describes it as Mrs May's "Brexit fightback" while the i draws a comparison to Margaret Thatcher with a headline that reads: "May tells EU: I'm not for turning".
But the Daily Telegraph says the prime minister is facing a showdown with her cabinet next week when ministers will call for a "Plan B" alternative to the Chequers proposals.
Italian MEP Roberto Gualtieri, who sits on the European Parliament's Brexit Steering Group, also expressed optimism that a solution will be reached.
He told BBC Newsnight: "I think that no deal is not an option. We are sure that the rationality will prevail."
In her televised statement on Friday, Mrs May said talks had reached an "impasse" and could only be unblocked with "serious engagement" from the EU side.
"Throughout this process, I have treated the EU with nothing but respect," she said. "The UK expects the same, a good relationship at the end of this process depends on it.
"At this late stage in the negotiations, it is not acceptable to simply reject the other side's proposals without a detailed explanation and counter proposals."
The pound's fall against the dollar and the euro deepened following Mrs May's statement.
Some Brexiteer MPs praised her for her comments. Jacob Rees-Mogg welcomed the "strong and forthright" speech but said she should abandon her Chequers plan and come forward with a Canada-style free trade agreement.
Conservative MP Andrew Bridgen - who previously called for a no-confidence vote on Mrs May - said she needed to "chuck" the Chequers plan.
"I think it could be a very, very rough ride for the prime minister when she finally realises how unpopular her Chequers proposals are, not only within the EU, but within the membership of the Conservative Party out in the constituencies," Mr Bridgen told BBC Newsnight. "It' s a grim time really.
In her speech on Friday, the PM said both sides were still "a long way apart" on two big issues: the post-Brexit economic relationship between the UK and EU, and the "backstop" for the Irish border, if there is a delay in implementing that relationship.
Both the UK and the EU want to avoid a hard border - physical infrastructure like cameras or guard posts - between Northern Ireland and the Irish Republic but cannot agree on how.
The two options being offered by the EU for the long-term relationship - for the UK to stay in the European Economic Area and customs union or a basic free trade agreement - were not acceptable, Mrs May said.
Mrs May says her plan for the UK and EU to share a "common rulebook" for goods, but not services, is the only credible way to avoid a hard border.
Arlene Foster, leader of Northern Ireland's DUP, who Mrs May relies on for a Commons majority in key votes, said the prime minister was "right to stand firm in the face of disrespectful, intransigent and disgraceful behaviour by the European Union".
Labour leader Jeremy Corbyn said the prime minister's negotiating strategy "has been a disaster" and said "political games from both the EU and our government need to end" to avoid a no-deal scenario.
Labour wants to see the UK join a customs union with the EU after Brexit, but remain outside of the single market.

Conservative MPs should back Theresa May's deal this week or risk losing Brexit altogether, Foreign Secretary Jeremy Hunt has warned.
There was "wind in the sails" of those opposing Brexit and the consequences for the party will be "devastating", if it is not delivered, he said.
MPs will vote again on the deal on Tuesday, after rejecting it in January.
Labour's John McDonnell said it looked like the PM had failed to secure any changes and it would be rejected again.
The UK is due to leave on 29 March, although Parliament has yet to agree the terms of withdrawal.
MPs will vote for a second time on Tuesday on the withdrawal deal Mrs May has negotiated with the European Union - after rejecting it by a historic margin in January.
If they reject it again, they will get a vote on leaving without a deal, and if that fails, on delaying the exit date.
Many Conservative Brexiteers voted against the deal in January over concerns about the backstop - a controversial insurance policy designed to prevent physical checks on the border between Northern Ireland and the Republic of Ireland.
But there have been few visible signs of progress over the issue in continuing talks between EU and UK officials.
Mr Hunt told BBC One's Andrew Marr Show some MPs wanted to "kill" the deal, in order to delay Brexit, with the ultimate aim of getting another referendum on the issue.
"Within three weeks, those people could have two of those three things," he said, adding that Labour's position made the third more likely.
He said: "We are in very perilous waters, and people who want to make sure that we really do deliver this result need to remember that if it fails... they are going to say: 'There was a party that promised to deliver Brexit, we put them into No 10 and they failed', and the consequences for us as a party, would be devastating."
He added: "We have an opportunity now to leave on March 29, or shortly thereafter. And it's very important that we grasp that opportunity because there is wind in the sails of people trying to stop Brexit."
If Parliament approves Mrs May's withdrawal agreement next week and the UK leaves the EU on 29 March, it will begin a transition period, when the two sides will attempt to agree a comprehensive trade deal.
If a trade deal is not agreed by the end of the transition period, the "backstop" plan is designed to maintain an open border on the island of Ireland.
It would keep the UK in a "single customs territory" with the EU, and leave Northern Ireland in the EU's single market for goods.
But some MPs fear that - in its current form - the backstop may leave the UK tied to the EU indefinitely.
On Friday, Mrs May urged the EU to help her get the deal through by resolving concerns about the backstop.
But Shadow Chancellor John McDonnell told the BBC: "It looks as though she's bringing back the same deal so it looks as though we will have the same result and it will be thrown out."
He said the party's priority this week would be to stop Theresa May "driving through some sort of Brexit deal that will damage our economy and undermine jobs" and if that meant a delay to allow for a discussion about the deal Labour backs instead "so be it".
He also denied that Labour's support for keeping the option of another referendum open had been put on the backburner, adding: "If Parliament can't agree, if we have to break the logjam, yes, we will keep the option available of going back to the people."
And he said he believed that Labour's alternative Brexit deal could be agreed with the EU "within a matter of weeks" but said any delay requested should be "as long as is necessary".
Labour's policy is to seek a permanent customs union with the EU after Brexit, which would allow the UK "a say" in future trade deals. Mr McDonnell said the EU had "looked positively" on the proposal.
On Friday, the EU said it would give "legal force" to assurances it has already made about the withdrawal deal and its chief negotiator Michel Barnier tweeted that the UK would be free to leave a proposed single customs territory with the EU - provided Northern Ireland remained within it.
The leader of the House of Commons, Andrea Leadsom, said she was deeply disappointed by the EU's proposal, which has already been rejected by the UK government.
The Brexit Secretary it was "not the time to rerun old arguments".

Allowing the UK to unilaterally halt the Brexit process could lead to "disaster", judges at Europe's top court have been warned.
The European Court of Justice is deliberating on whether the UK can call off its withdrawal from the EU without permission from member states.
But lawyers acting for the EU said allowing countries to do so could create "endless uncertainty".
The case has been brought by a group of Scottish politicians who oppose Brexit.
They hope it will give clear guidance to the UK Parliament about the options open to it as MPs vote on the prime minister's Brexit deal - and that it will result in "no Brexit" being an alternative to either "no deal" or Mrs May's deal.
The UK government says it has no intention of calling off Brexit, and says the politicians bringing the case are using it as "ammunition" in their campaign to halt the withdrawal process.
The court also heard from lawyers representing the Council of the European Union and from the European Commission, who both argue that revoking Article 50 is possible - but that it would require unanimous agreement from the other 27 member states.
They are concerned that the case could set a precedent where other countries would be able to formally notify their intention to leave and then seek better terms from the remaining EU countries, before cancelling their withdrawal.
Analysis by Adam Fleming, BBC News in Luxembourg
There were two emotions on display in the ECJ's gold-encrusted courtroom: hope and fear. The UK government was worried that anything said about Brexit by European judges could be used as ammunition in the battle to bring down Theresa May's deal.
The EU fretted about Article 50 being re-written in a way that meant a country could announce it was leaving then change its mind again and again, creating a state of permanent anxiety. Or worse, using it as a tactic to secure a better deal at the EU's expense.
The campaigners who brought the case were just glad that the concept of Brexit being reversed had a very public airing so close to the vote on the deal by MPs.
Hubert Legal, the chief lawyer for the European Council, argued that allowing unilateral withdrawal could therefore lead to "disaster", of which "the main victim could be the European project altogether".
This was echoed by lawyers for the European Commission, who said states could act in an "abusive" manner by stopping and restarting the countdown clock, creating "endless uncertainty" - which the two-year time limit built into Article 50 was designed to guard against.
A four-hour hearing on Tuesday morning saw the full court of 27 judges consider the arguments in the case.
The court has said it will aim to decide "quickly" on the case, but has not yet set a date for doing so.
The case is being considered against the backdrop of Prime Minister Theresa May fighting to sell her draft Brexit deal to MPs, ahead of a vote in the Commons in December.
The UK will leave the EU on 29 March under the terms of "Article 50", a two-year notification of withdrawal which MPs triggered in March last year.
The case has been brought by a cross-party group of Scottish politicians including Green MSPs Andy Wightman and Ross Greer, MEP Alyn Smith and MP Joanna Cherry of the SNP, and Labour MEPs David Martin and Catherine Stihler.
They say it could give MPs an extra option when considering whether to approve the draft deal or not, because it could keep alive the prospect of calling off Brexit
Mr Wightman said the question was "vital", saying that "the chaos around Brexit shows no sign of being resolved" and that the UK parliament "must be fully informed of all of its options".
Aidan O'Neill QC, who is representing the Scottish politicians, told the court that European lawyers were inviting the judges to act "unconstitutionally and in contravention of the rule of law by reinterpreting the treaties".
He said: "It cannot be in the interest of the union as a whole to force a member state to leave the union against the wishes of the people.
"The union's wider interest lies with member states remaining in the EU when their peoples wish to do so."
The UK government has opposed the case being heard from the outset, but failed to prevent it going before judges in Luxembourg after a series of appeals.
The UK government's position is that the court has "long refused for very good reasons" to answer hypothetical questions which could interfere with domestic politics. They argue that because "the UK does not intend to revoke its notification", the question of whether it can do so unilaterally is a hypothetical one.
Ms Cherry raised the case and the issue of revoking Article 50 with Mrs May in the Commons on Monday, prompting the prime minister to say that "it is not going to happen because it is not government policy".
Advocate General Lord Keen, who is representing the UK government, argued in court that the case was being used as "ammunition" by opponents of Brexit, and said the judges should find it inadmissable.

Gina Miller is the businesswoman and campaigner who has twice led legal challenges against the government and won.
Her first victory came in September 2017, when the Supreme Court ruled in favour of giving MPs a say over triggering Article 50 - the legal mechanism taking the UK out of the EU.
Her second came on Tuesday, when the Supreme Court ruled that Boris Johnson's decision to suspend Parliament was unlawful.
Her success in the courts has come at a price - she has become a hate figure for many Brexit supporters and has had to employ round-the-clock security after threats to her life.
She says she does not want to block Brexit, but is standing up for Parliamentary democracy.
Speaking outside the Supreme Court after the ruling on Tuesday, she said: "Today is not a win for any individual or cause, it's a win for Parliamentary sovereignty, the separation of powers and the independence of our British courts.
"Crucially, this ruling confirms that we are a nation governed by the rule of law."
Mrs Miller is not officially aligned to any political party, having spurned the advances of the Liberal Democrats, who rapturously received a speech she gave at their 2018 party conference.
A 54-year-old investment manager and philanthropist, Mrs Miller was born in Guyana and educated in Britain.
She went first to an exclusive all-girls private boarding school, Roedean, on the outskirts of Brighton, at the age of 10, then to Moira House Girls' School, in Eastbourne, East Sussex.
Afterwards, she studied law at the University of East London, but left before completing her degree.
Mrs Miller went on to start a successful marketing consultancy business with clients including private medical specialists in Harley Street in London.
In 2009, she used the money she had made in marketing to co-found an investment firm supporting smaller charities.
"I realised then it was my money, I could do what I wanted with it and so I used that money to get involved in social justice," Mrs Miller told Unfiltered with James O'Brien last year.
And in 2012, the businesswoman began the True and Fair Campaign, which campaigned for greater transparency in the City of London's fund management industry.
According to an interview with the Financial Times in 2016, this led some in the industry to label her the "black widow spider".
Speaking about a time she asked three men at an industry party why they were staring at her, she told the paper: "One of them replied that I was a disgrace and that my lobbying efforts would bring down the entire City."
Mrs Miller launched her first Brexit legal case with London-based Spanish hairdresser Deir Tozetti Dos Santos and the People's Challenge group, set up by Grahame Pigney - a UK citizen who lives in France.
Backed by a crowd-funding campaign, they argued the government could not invoke Article 50 of the Lisbon Treaty - starting the formal process of the UK leaving the EU - without seeking approval from Parliament.
Mrs Miller argued only Parliament could make a decision leading to the loss of her "rights" under EU law.
But she stressed the challenge was not an attempt to overturn the referendum decision, telling BBC Radio 4's Today programme: "We are all leavers now."
In November 2016, three High Court judges ruled Parliament had to vote on when the process could begin.
Speaking after her victory, Mrs Miller told the BBC the case was about scrutinising the details of Brexit, such as "how we leave, how they're going to negotiate, the directions of travel the government will take".
And she said the legal challenge was about more than Brexit, arguing that it was "verging on dictatorship" for a prime minister to be able to take away people's rights without Parliament's consent.
The government appealed, and the case went to the Supreme Court the following December, but the 11 judges rejected it by a majority of eight to three.
Following the successful legal challenge, Mrs Miller suffered online abuse, including rape and death threats against her and her family.
She told James O'Brien: "It has changed the way we live our lives, and the conversations we have with the children".
"We use humour a lot because that's the only way to get through it", she told him.
In July 2017, an aristocrat who wrote a Facebook post offering £5,000 to anyone who ran over Mrs Miller was sentenced to 12 weeks in prison.
Describing the businesswoman as a "boat jumper", Rhodri Colwyn Philipps - the 4th Viscount St Davids - wrote: "If this is what we should expect from immigrants, send them back to their stinking jungles."
The peer claimed the comments were "satire" and a "joke".
But the judge, who said the post effectively put a "bounty" on Mrs Miller's head, found him guilty of two charges of making menacing communications.
Later that year, Mrs Miller was named as Britain's most influential black person.
"It's amazing to get an accolade when what I've done has solicited a huge amount of abuse," she said on receiving her title.
"To have somebody acknowledge me is extraordinarily kind and counters a lot of what I still get on a daily basis."
Despite the backlash, Mrs Miller went on to launch a second challenge against the government to "defend Parliamentary sovereignty".
After Mr Johnson announced in August that he would suspend Parliament for five weeks, Mrs Miller challenged the legality of the decision at the High Court.
She argued that Parliament would be "silenced" for an "exceptional" length of time in the critical period before the 31 October Brexit deadline.
She initially lost her case, but in Scotland, a separate legal challenge succeeded, with judges taking the view that the suspension was unlawful.
The UK government appealed to the Supreme Court against the Scottish judgement, and the two cases were then heard together.
The court unanimously ruled in favour of Mrs Miller's appeal and against the government's.
Judges said it was wrong to stop MPs carrying out duties in the run-up to the Brexit deadline on 31 October.
After the ruling Mrs Miller told reporters the ruling showed the government "will push the law, they will push the constitution and they will even bend it to get their own way".

We asked for your questions and received more than 1,100 responses within five hours. Below are some answers to our most frequently asked questions.
The court ruling does not mean the end of Brexit.
The case was about the government's right to trigger the formal two-year process of leaving the EU without there being a vote in Parliament.
The government is going to appeal against the decision, but, as things stand, the ruling means MPs and lords will have to give their go-ahead before Prime Minister Theresa May starts her negotiations on the UK's exit from the European Union.
Theoretically, they could decide not to give the go-ahead - but, in practice, that is seen as highly unlikely given that a majority of people who voted in the June referendum voted for the UK to leave the EU.
Legal affairs commentator Joshua Rozenberg said the decision had been based on the argument the government could not use its executive powers because it would mean effectively overturning an act of Parliament.
Triggering Article 50 would eventually lead to the UK leaving the EU, which effectively takes away rights granted by Parliament, such as the right to free movement in Europe.
The High Court ruling effectively defined the limits of government power by reiterating that Parliament is sovereign - it can create laws and only Parliament can take them away.
We do not know yet, but it may try to repeat the argument that its prerogative powers allow it to trigger Article 50 because that in itself does not mean an immediate change to UK citizens' EU rights.
Paragraph 13 of the ruling essentially states that a parliamentary motion is not enough to satisfy the terms of Brexit.
UK membership is bound not in prerogative power, but in the 1972 EU Communities Act, and therefore needs primary legislation to be taken away.
Brexit Secretary David Davis said: "The judges have laid out what we can't do and not exactly what we can do, but we are presuming it requires an act of Parliament."
The EU referendum was advisory - as was discussed in the court ruling on Thursday.
It points to the "basic constitutional principles of parliamentary sovereignty and representative parliamentary democracy" in the UK, which "led to the conclusion that a referendum on any topic can only be advisory for the lawmakers in Parliament unless very clear language to the contrary is used in the referendum legislation in question".
"No such language is used in the 2015 Referendum Act," it adds.
Possibly, but it would be surprising if it was, according to Joshua Rozenberg, because the case is about the UK's constitutional requirements, not EU law.
The lead claimant in the case is investment manager and philanthropist Gina Miller, who launched the case alongside London-based hairdresser Deir Dos Santos and a group called the People's Challenge Group, which is backed by a crowdfunding campaign. You can Article 50 of the Lisbon Treaty is usually considered to be the only legal way to leave the EU. It states that a country that decides to leave the EU has two years to negotiate "arrangements for its withdrawal, taking account of the framework for its future relationship with the union". This will involve unravelling UK-EU treaty obligations; such as contributions to EU budgets, and holding talks on future trade relations. However some have suggested that the UK could leave the EU by other means - by amending EU treaties or repealing UK legislation. Douglas Carswell, then a Conservative MP and now UKIP, tried to introduce a European Communities Act 1972 Repeal Bill in 2012.
Although negotiations over international treaties are normally powers reserved to the UK Parliament at Westminster, because leaving the EU could involve the removal of people's rights under EU law, the devolved administrations want to have their say in the Article 50 process.
Ever since devolution to Scotland, Wales and Northern Ireland began in 1999, Westminster normally seeks the agreement of the devolved parliaments and assemblies if it is legislating on devolved matters. While Westminster debates a bill, legislative consent motions are passed in Wales, Scotland and Northern Ireland. Political difficulties could arise should they choose to vote on legislative consent motions relating to any bill to enact Article 50.
On Friday the Welsh Assembly's senior legal adviser, Mick Antoniw, said he would seek to make representations to the Supreme Court during the government's appeal about the potential impact on Wales. SNP MPs may decide to vote against triggering Article 50 at Westminster - Scotland's First Minister Nicola Sturgeon said they would "vote in line with the wishes and the interests of the Scottish people", potentially delaying the process.
A High Court case in Belfast last week saw a cross-party group of MLAs attempt to prevent Article 50 being triggered without a Parliamentary vote or a vote in the Northern Ireland Assembly. That case was rejected but those behind it are taking it to the Supreme Court.
Much depends on whether the government wins its appeal to the Supreme Court and, if not, to what extent new legislation about triggering Article 50 is delayed by questions and amendments in Parliament.
Theresa May announced the Great Repeal Bill - which would abolish the 1972 European Communities Act and transpose all relevant EU law on to the UK statute book after the UK leaves the EU - on the day she said she wanted to trigger Article 50 by the end of March 2017. The High Court ruling that the government cannot enact Article 50 without the backing of Parliament could delay that timetable.
Many British expats were annoyed at not being allowed to vote in the EU referendum and there are moves by the government to scrap, by 2020, a rule that says Brits who have not lived in the UK for 15 years cannot vote in UK elections.
However, this ruling does not stop the 23 June vote to leave coming into force, nor does it mean a second referendum, so expats who wanted to vote to remain in the EU are unlikely to be able to vote on the issue again.
Even if there were a second vote on the issue, the government's "votes for life" proposal refers to UK parliamentary elections and says the "franchise for referendums will continue to be held on a case-by-case basis" - so it is not clear whether, in the event of a hypothetical second vote on Brexit, expats would get a vote anyway.
This has not yet been put to the test as no country has triggered Article 50 before and there seems to be some confusion. The Scottish cross-bench peer who wrote it, Lord Kerr, told the BBC this week he believed it was "not irrevocable" and, even if the process had begun, a member state could still choose to remain in the EU. However the High Court ruling states that it was "common ground" between both sides that Article 50 "cannot be withdrawn once it is given".
Once Article 50 is triggered, the UK has up to two years to negotiate a deal with the EU. But what if it runs out of time?
Robyn Munro, from the Institute for Government, says there are three options: 1) the UK could get an extension on the negotiating period if all EU members agree, 2) the UK could try for an "interim deal" while negotiations continue after two years - perhaps with some access to the single market but losing its influence in the EU and 3) the UK could leave without any agreement, and treaties would cease to apply. This would mean falling back on WTO rules for trade but there would be much uncertainty over other areas such as the rights of UK citizens who live and work in the EU, EU citizens in the UK and whether UK airlines would have the right to fly into EU airspace.

In a crisis there can be opportunity.
This is now a crisis - the rules that traditionally have preserved governments are out of the window.
The prime minister has been defeated again. Her authority - if not all gone - is in shreds.
But for Number 10 there's an opportunity too, because MPs will soon be presented with a new choice - back the PM's deal, which has already been defeated twice, or accept the chance of a delay to Brexit.
This isn't the choice of a government that's in control. But the tactic is to make the best of chaos.
To use nerves among Brexiteers to shove them towards accepting Theresa May's deal in the absence of another solution with no other agreed alternative - yet.
The prime minister is beginning another day not sure of where it will end.
MPs are bristling to push their own different solutions - none of which she or Parliament as a whole, let alone the public, is ready to accept.
Yet even if this pandemonium strangely leads the way to order, to a smooth departure from the European Union, there's a different question: could a functioning administration ever again exist under the present cast?

A new plan for post-Brexit customs arrangements will be a "significant step forward", a Downing Street source has promised.
The proposal, to be presented to ministers on Friday, will offer "the best of both worlds" - an independent trade policy and friction-free trade, the source added.
But no details have yet been revealed about how it will work.
Ministers have so far failed to agree what type of customs model to pursue.
Friday's Chequers summit, which will be followed by a White Paper setting out more details, is aimed at finalising the UK's preferred path which can then be put to the EU.
BBC political editor Laura Kuenssberg said some ministers appeared not to have been involved in drawing up the new proposal, which is being called a "third way" after two previous proposals divided opinion.
Earlier, government divisions were underlined when Foreign Secretary Boris Johnson intervened in defence of Eurosceptic backbencher Jacob Rees-Mogg, who had been accused by two other foreign office ministers of "threatening" Theresa May over Brexit.
The UK is due to leave the EU on 29 March 2019, and negotiations are taking place on what the future relationship between the UK and the EU will look like.
Key things that have yet to be agreed are how the two sides will trade with each other in years to come - and how to avoid new border checks between Northern Ireland and the Republic, which is a member of the EU.
Before reaching agreement with the EU, Mrs May needs to resolve splits within her cabinet on the shape of Brexit.
BBC political editor Laura Kuenssberg
The immediate problem with the "new plan" is whether or not it really exists.
Because while Number 10 says it does, ask other people in government and they are not quite so sure. Ministers who you might have thought would be aware of the detail like - oh, you might imagine - the Brexit secretary had not agreed the lines, before Number 10 made their intervention.
And it's said tonight that the reason he has not been involved in agreeing the "new plan" is because it does not actually exist yet. The customs decision expected in some parts of government therefore is what has been anticipated for some time as "max fac plus" - a souped up version of the proposal that originally won the day in the Brexit subcommittee what feels like a lifetime ago - with, you assume, a long lead-in time while the technology is made to work.
Baffled? Quite possibly so. But it's perhaps only safe to say that four days before ministers are expected to actually make some final decisions, all is not precisely as you might have expected.
Read the rest of Laura's blog
Earlier, she urged the EU to consider her blueprint for future relations "seriously" as she updated MPs on last week's Brussels summit.
Pressed to give more detail of her plans as she took questions in the Commons, Mrs May said she hoped her vision for the UK's future relations would address the "real differences" on the issue of the Irish border.
"The EU and its member states will want to consider our proposals seriously," she said.
"We both need to show flexibility to build the deep relationship after we have left that is in the interests of both our peoples."
Labour leader Jeremy Corbyn said the cabinet was irrevocably split between different Tory factions.
But Mrs May rejected calls to "pick a side" between Remainers and Brexiteers, saying: "I have picked the side of the British people and these are the ones for whom I will deliver."
She is also due to have talks in Berlin with German Chancellor Angela Merkel ahead of the Chequers meeting.
The BBC's Brussels reporter Adam Fleming
Sources in both the European Council and the European Commission deny they have seen a draft of the UK's Brexit White Paper.
Officials in Brussels predict it will mostly be a compilation of existing British positions - "a best of" is how one described it.
Theresa May "hinted" at the publication of the document when she addressed EU leaders at their summit last week but she did not elaborate on its contents.
Ministers from the remaining 27 member states are planning to respond to the White Paper at a meeting of the General Affairs Council on 20 July.
EU officials expect to be going through the document until the end of July.
The government has so far talked publicly about two potential customs options.
One, a customs partnership, would mean the UK applies the EU's own tariffs and rules of origin to all goods arriving in the country and then hands over what was owed for goods that subsequently end up in the EU.
The other, known as maximum facilitation or max-fac, aimed to employ new technology to remove the need for physical customs checks where possible.
It is understood both options have been deemed practically or politically undeliverable and a third option is on the table, believed to involve "alignment" with the EU in regulations covering trade in goods but a looser relationship for services.
Writing in the Daily Telegraph earlier, Mr Rees-Mogg said he and other members of the 60-strong group of Eurosceptic Tory MPs he leads, known as the European Research Group, would reject a deal that did not amount to a clean break with the EU.
Mr Rees-Mogg said a deal which restricted the UK's ability to make trade agreements with other nations or control migration could not be accepted and Mrs May "must stick to her righteous cause and deliver what she has said she would".
But, speaking in the Commons, pro-EU MP Anna Soubry said the public were tired of what she said were continual "fudges" on key questions and urged Mrs May to stamp her authority once and for all.
And her colleague Nicky Morgan said Mrs May "would not be thanked for the mess we will end up in" if the government did not prioritise the needs of the economy in a "pragmatic, sensible, flexible" Brexit.
The Democratic Unionist Party, whose support Theresa May needs to have a majority in key Commons votes, said it would not support any deal which did not give the UK full control over its borders.
"We don't give blank cheques to anybody," its Westminster leader Nigel Dodds said after meeting the PM for an hour in Downing Street.
"We want to see a proper Brexit which fulfils the referendum result but we have been very clear that it has to be on the basis of the whole of the UK leaving the EU as one."
He accused Dublin and other European capitals of trying to "bully" the UK and using the issue of the Northern Irish border to "create an outcome which is to their liking", adding "they won't succeed in that".

The EU has finally announced its informal approval of a new Brexit extension: a full three months, running until 31 January, as suggested in the UK prime minister's extension request.
But what an excruciatingly long and confusing political dance to get there. And the dance is not over yet.
To become a formal offer, the Brexit extension still needs to be accepted by Prime Minister Boris Johnson. This is EU law and an unavoidable part of the procedure. But how uncomfortable for the prime minister who sought to distance himself as much as possible from the extension, previously promising that he would rather die in a ditch than request one.
The EU is also attaching some extra wording to the extension. Brussels wants the UK to realise that this is a "flextension": the UK does not need to stay in the full three months; instead, it can leave as soon as its parliament and the European Parliament have ratified the new Brexit deal. The extension text cites 1 December and 1 January as possible "early out" dates.
The EU extension text also reminds the UK that, until it leaves, it remains a fully paid-up member of the EU, including all the rights and obligations that go along with membership.
A new European Commission starts work in roughly a month's time. The new Commission President, Ursula von der Leyen, is insisting the UK nominate a new commissioner so as not to undermine the legal workings of the EU as long as the UK remains in it.
Mr Johnson is obliged by UK law to accept the new Brexit delay. But EU leaders take nothing for granted anymore. Under EU law, a no-deal Brexit is still possible as of midnight Central European Time (23:00 GMT) on Thursday.
Now, if and when the prime minister despatches his ambassador to the EU to submit a letter of UK acceptance of the extension, then Brussels says it still needs another 24 hours. This is because the text was agreed at EU ambassador level. It still needs to be signed off by the "grands fromages" - leaders in all EU capitals.
And why did it take the EU so long to make a decision? Early last week, there were confident assertions being made in Brussels that the UK's three-month extension request would be approved.
Yet what followed was a seemingly shambolic make-it-up-as-you-go-along EU timetable, where "announcement day" moved from last Thursday to Friday to this Tuesday, Wednesday and now Monday.
What initially slowed EU leaders down last week was France, the one EU country deeply opposed to the three-month extension. President Emmanuel Macron agreed with Boris Johnson that a shorter, sharper extension would better focus the minds of MPs in Westminster on the newly negotiated Brexit deal.
After more than three years of Brexit confusion and indecision in Parliament, France feared a longer extension would give MPs the space to keep chasing their tails instead of coming to conclusions.
UK political discourse at the end of last week also interfered with the EU's decision-making process. Government and opposition MPs kept deferring questions about holding a general election, saying: "We'll decide when we hear from the EU about the length of the extension they're going to grant."
EU leaders did not want their decision about a Brexit delay to be politicised. Since a vote was scheduled in Westminster on Monday on Boris Johnson's push to hold a December general election, Brussels said it would announce its extension decision after that.
But two key issues moved ahead of time over the weekend, meaning that, in the end, the EU felt emboldened to make its announcement ahead of the Westminster vote:
And after the extension has been signed off this week, Brussels will watch from the sidelines, arms folded, as the next moves are decided in Westminster.
Hope runs deep in the EU that Brexit will now finally be decided by UK politicians and voters, but there is a lingering sense of doubt here too.
Based on more than three years of false dawns in the process, the EU knows there is a distinct possibility, come January, that the spectre of yet another Brexit extension could rise once again.

A commemorative 50p coin marking the UK's departure from the EU has been unveiled by Chancellor Sajid Javid.
The coins bear the inscription "Peace, prosperity and friendship with all nations" and the date of 31 January.
Mr Javid had first ordered production of the coins in advance of the UK's original 31 October departure date.
But the Brexit delay meant about a million coins had to be melted down and the metal put aside until a new exit date was confirmed.
About three million Brexit coins will enter circulation around the UK from Friday, with a further seven million to be added later in the year.
Mr Javid, who is Master of the Mint, was given the first batch of coins and will present one to Prime Minister Boris Johnson this week.
As part of the launch of the coin, the Royal Mint will open the doors of its south Wales HQ for 24 hours on 31 January (from 00:01 to 23.59) to let people strike their own commemorative Brexit coins.
Mr Javid said: "Leaving the European Union is a turning point in our history and this coin marks the beginning of this new chapter."
The European Parliament is expected to approve the Withdrawal Agreement on Wednesday, after the PM this week signed the treaty paving the way for the UK to leave on 31 January.

It's not even 24 hours since the PM called the general election she said she wouldn't call.
It's the opposite of Gordon Brown's "election that never was", rather the "election that wasn't meant to be".
Much will be written about her motivations for the U-turn, the change of heart that led her to this point. The long-term view of her motivation will in time be coloured by the eventual result of course.
But as the unofficial day one of this campaign draws to a close, some things are clear.
For months there has been a pretty straightforward balance sheet of advantages and disadvantages to holding an early poll. Theresa May believed it tipped to holding firm.
There were plenty of reasons for going early - most temptingly making the most of Labour's weakness to grab dozens of seats.
It would free Theresa May from the strictures of the 2015 manifesto - she's already proved she doesn't feel much constrained by that - which no one who remains in government had involvement in putting together.
It would give her her own mandate, even though PMs are not directly elected. It would draw a line between her leadership and David Cameron's, once and for all.
And with a likely majority, IF the polls are correct, it would make it easier for her to get her Brexit plans through Parliament, give her more freedom to pursue her other - some controversial - plans like reintroducing grammars, and strengthen her hand with EU leaders as she gets down to negotiations.
Going early could also minimise the potential fallout over the Tory expenses saga - a bad hangover from the 2015 election.
In the negative column:
Until only a few days ago it was those arguments that held sway.
Theresa May has shown time and again that she is willing to change her mind when the facts change.
For example, she and her chancellor dropped a major plank of his Budget in only a week when they saw resistance, and the government junked a review of the powers of the House of Lords.
Her public argument for calling an election - that it was resistance from the opposition and the Lords over Brexit - does not quite tell the full story.
Parliament has been tricky for the PM, but certainly not impossible.
Notwithstanding that, nor the factors that have created strong political arguments for taking the plunge in the last couple of months, senior government sources point to a specific factor that changed the prime minister's calculation.
The end of the likely tortuous Article 50 negotiations is a hard deadline set for March 2019.
Under the Fixed Term Parliaments Act, that's when the Tories would be starting to prepare for a general election the following year, with what one cabinet minister described as certain "political needs".
In other words, the government would be exposed to hardball from the EU because ministers would be desperate to avoid accepting anything that would be politically unpopular, or hold the Brexit process up, at the start of a crucial election cycle.
As one insider put it: "We'd be vulnerable to the rest of the EU in 2019 because they know we'd have to move fast."
Ministers say that's the central reason for Mrs May's change of heart because "if there was an election in three years, we'd be up against the clock".
By holding the election now, Theresa May hopes she gains a fresh start on the political clock on Brexit, even though the Article 50 process still has a deadline of only two years.
This gives what was described as "flexibility over the logistics of Brexit… we don't have to pretend we can do it all in two years".
That's not to say for a second this means departure from the EU will be held up. The Article 50 process will proceed, the government says, exactly as planned.
But, if the Tories win, an early election may have bought ministers some valuable breathing space to work out what the UK really looks like outside the EU.
They'll have, in theory, three years after exit for things to settle down before the public get another chance to have their say.
That timetabling question was not her only reason, as outlined above.
But after the EU's initial brush off after the Article 50 letter, that argument became more compelling.
The PM's conclusion was that the best way of her going into those negotiations in as strong a position as possible, was by taking advantage of the window between the French and German elections before the EU gets down to proper business.
A hypothetically bigger majority of course also acts to neutralise the cruelly dubbed "Remoaners" in her own party, and the far larger, and much more powerful, group of ardent Leavers who have been able to exert a lot of pressure.
But while the polls suggest an early election could make many of her political problems disappear, polls prove nothing.
Politics in 2017, as we've discussed again and again, is unpredictable and taking bets is a fool's game. The reasons Theresa May hung back from an early election haven't disappeared.
PS: Westminster's guessing game has been who knew, and when.
No one will confirm officially on the record. For what it's worth, sources tell me that David Davis and Philip Hammond were the only ministers who were extensively consulted.
Both Boris Johnson and Amber Rudd were told before Tuesday morning's cabinet meeting. But there were ministers around the cabinet table who had no idea and who were, it's said, visibly shocked when Mrs May told them.
The cabinet was kept in the cabinet room during the announcement, and watched it on TV.
The mood was apparently very enthusiastic, with one moment of huge laughter when the wifi link that was playing her announcement on the screen in the street just outside broke down and the PM suddenly went to black.
Apparently the glitch was sorted within a few seconds, but her colleagues will hope the PM is better at running an election campaign than sorting out the Number 10 broadband.

Chancellor Philip Hammond has insisted that the prime minister's Brexit deal is better than remaining in the EU.
He said the deal respected the result of the 2016 referendum and offered "the best compromise possible".
European Council President Donald Tusk has recommended that the EU approve the deal at a summit on Sunday.
It comes after Spain, which threatened to miss the summit, was reassured over objections it had raised about Gibraltar.
Spanish Prime Minister Pedro Sanchez has now received enough reassurances from the UK government over the issue.
Mrs May flies into Brussels later to hold talks with top EU officials, ahead of the summit.
The UK is scheduled to depart the EU on 29 March 2019.
The terms of the UK's withdrawal have been under negotiation since June 2016 following a referendum in which 51.9% voted to leave the EU.
Even if the EU approves the deal, it still has to be passed by the UK Parliament, with many MPs having stated their opposition.
Arlene Foster, the leader of Northern Ireland's Democratic Unionist Party (DUP), has already stated the party will not back the Brexit deal - and is expected to reiterate her position at this weekend's annual conference in Belfast.
She will say the withdrawal agreement contains arrangements that are not in Northern Ireland's long-term economic or strategic interests.
Mrs May relies on the DUP, whose 10 MPs help the minority Conservative government to pass legislation.
The DUP has threatened to look again at the agreement with the Conservatives if the Brexit deal gets through Parliament.
DUP Chief Whip Jeffrey Donaldson denied the party would walk away from its agreement - but told the BBC the party was "very unhappy" with the withdrawal agreement.
Philip Hammond told Today he was hopeful of a solution with the DUP.
The deal on offer was the "best way of Britain leaving the EU with the minimum negative impact on the economy," he said.
The chancellor said the deal was better than remaining in the EU because it honoured the referendum result and offered "the best compromise possible... satisfying both sides" of the Brexit argument.
"If we want this country to be successful in the future, we have got to bring it back together after this process," he said.
By Leila Nathoo, BBC political correspondent
Ministers' hard sell of the Brexit deal continues - this morning it was Philip Hammond's turn.
He's been trying to reassure the DUP over their concerns about the Irish border - but he also had a message for MPs thinking of voting against the deal in the Commons.
Don't - or chaos will be unleashed.
Warnings about the economic consequences of a Parliamentary rejection will remind some of what was dubbed 'Project Fear' during the referendum campaign.
The chancellor's suggestion that there is no alternative can be seen as a dismissal of those critics - the DUP, Tory Brexiteers - who think there is still a chance of renegotiation.
Meanwhile, former Northern Ireland secretary Theresa Villiers - a Leave campaigner in 2016 - has said she will vote against the withdrawal agreement.
"I do not believe it is in the national interest," she told Today.
She said "every effort should continue to be made to try and reach a better agreement" but failing that, Theresa May "should walk away".
But Mr Hammond warned that a no-deal Brexit would unleash "economic chaos".
"If the meaningful vote [in Parliament] is lost we are in uncharted territory," he said.
On Saturday, Mrs May will meet the president of the European Commission, Jean-Claude Juncker, and European Council President Donald Tusk for talks.
Then on Sunday, EU leaders will meet for the special Brexit summit. They will be asked to approve two key Brexit documents:
There is no formal vote on Sunday but the EU expects to proceed after reaching a consensus.
Spain raised last-minute objections to how the issue of Gibraltar - a British Overseas Territory with 30,000 residents - had been handled in the Brexit talks so far.
Spain has long-held ambitions to bring the territory back under Spanish rule, and there's growing concern about how their economic ties with the territory will be affected by Brexit.
Although one country on its own cannot stop the withdrawal agreement being approved, there is "no way the EU can rubber-stamp a text when an existing member is so strongly opposed", said BBC News Europe editor Katya Adler.
France, Denmark and the Netherlands had raised concerns over what the political declaration said about fishing rights in UK waters - but this issue is understood to have been resolved.
If the EU signs off the withdrawal deal, Mrs May will then need to persuade MPs in her own Parliament to back it.
A vote in Parliament is expected to happen in December.
Labour, the SNP the Liberal Democrats, the DUP and Plaid Cymru have all said they will vote against the government's deal, as well as many Conservatives.
On Friday, the PM said the UK should not hope for a "better deal" from the EU if MPs reject her Brexit agreement.
But she declined to say whether the UK would be better off outside the EU, saying only it would be "different".
Meanwhile, the Telegraph said it has seen leaked Cabinet papers which suggest the PM is planning to "reframe the Brexit debate around migration" - by planning restrictions on low-skilled migrants coming to the UK - in a bid to attract the support of Brexiteers.
Yes. After the 2017 general election, Mrs May's Conservative Party got 318 seats - four short of the number she needed to rule with a majority government.
The DUP formed a confidence and supply agreement with the Tories, promising that its 10 MPs would vote with the government, and therefore enable it to win key votes in Parliament.
The DUP opposes the Brexit deal because of the "backstop" - the last resort back-up plan to make sure a hard border between Northern Ireland and the Republic of Ireland never happens.
It will only come into effect if the UK and EU fail to agree a long-term trade deal. But the backstop would mean that Northern Ireland - but not the rest of the UK - would still follow some EU rules on things such as food products.

International Trade Secretary Liam Fox has refused to back Chancellor Philip Hammond's warning that a "no-deal" Brexit could damage the economy.
Speaking on the BBC's Andrew Marr show, he said: "This idea that we can predict what our borrowing would be 15 years in advance is just a bit hard to swallow."
Treasury analysis estimates that by 2033 borrowing would be around £80bn a year higher under a "no-deal" scenario.
It also forecasts no deal could mean a 7.7% hit to GDP over the next 15 years.
Asked by Andrew Marr whether he accepted the figures, Mr Fox said: "Can you think back in all your time in politics where the Treasury have made predictions that were correct 15 years out. I can't.
"They didn't predict the financial crisis. No-one could."
Pressed on whether he agreed with the chancellor, Mr Fox said: "I don't believe that it's possible to have a 15-year time horizon on predictions of GDP."
"So the answer's no," said Marr.
Divisions have deepened within the party in recent months as Brexiteers accuse Mr Hammond - who is seen to be pushing for a softer version of Brexit - of embarking on "another instalment of dodgy project fear".
Meanwhile, there is growing pressure on the prime minister to win support for her Brexit plan, known as the Chequers agreement.
The plan would see the UK agreeing a "common rulebook" with the EU for trading in goods, in an attempt to maintain friction-less trade at the border.
But critics say it will leave the UK tied to EU rules and prevent Britain from striking its own trade deals in years to come.
In his interview, Mr Fox said he was behind the Chequers plan and and could not imagine many things worse than remaining in the EU.
By Susana Mendonca, BBC political correspondent
The prime minister may be promising to stand firm on no second referendum but that is not stopping opponents in her own party from gearing up to take down her Chequers plan for Brexit.
International Trade Secretary Liam Fox - who's stayed inside the PM's camp - has warned that there's no point in trying to unseat Theresa May because "changing the leader doesn't change the party arithmetic".
While David Davis, who resigned over Chequers, has suggested that the prime minister limited his influence over the negotiation process. He said while he was the Brexit secretary, whether he "controlled events" was "another matter".
Mr Davis has never been one to shy away from making his views known and now that he is on the outside of the tent - he will join the chorus of Brexiteers doing exactly that, as Mrs May heads into the final stretch before she does or does not get a deal on Brexit.
In an article for the Sunday Telegraph, Theresa May has insisted she would not be forced into watering down her Brexit plan during negotiations with the EU.
The PM wrote that she would "not be pushed" into compromises that were not in the "national interest".
But David Davis, the former Brexit secretary who resigned over the Chequers agreement, said the caveat - "except in the national interest" - was an "incredible open sesame to all".
Also interviewed on the Marr show, he admitted he would vote against Mrs May's plan in any Commons vote, saying it would be "almost worse" than staying in the EU.
Another Conservative MP, Nick Boles - a former minister who backed Remain - said the Chequers policy had "failed" and he could no longer support it.
Also writing in the Sunday Telegraph, he said the EU was treating the plan as "an opening bid", and the UK was facing "the humiliation of a deal dictated by Brussels".
In his interview, David Davis said concerns over maintaining a soft border between Northern Ireland border and the Republic had been "heavily overemphasised" in the past.
"This is a much more straightforward issue to deal with if we choose to, if we put the political will behind it, we and the Irish Republic, the two together," he said.
However he said he did agree with Mrs May that a second referendum should not take place.
In her article, she said it would be a "gross betrayal of our democracy and... trust" to "give in" to those calling for another vote.
Her objection to it comes as a movement pressing for another referendum - the People's Vote - continues to gather high profile backers, including Sir Patrick Stewart and BBC football anchor Gary Lineker - as well as donations.
One supporter, Labour MP Chuka Umunna, said the impetus had shifted toward a public vote over the summer and it would be a "betrayal of democracy" for Mrs May "to force a bad deal - or no deal - on Britain without giving the public the chance to have a final say".

The Democratic Unionist Party's (DUP) bottom line has always been that any new Brexit arrangements should not separate Northern Ireland from the rest of the UK, economically or constitutionally.
Under the Stormont assembly's cross-community voting rules, contentious measures require a majority of both unionists and nationalists in order to pass.
The DUP had hoped to secure an upfront Stormont vote to approve the new arrangements.
But it's understood that the current proposals would give Stormont a say four years after the end of the transition period - that would mean 2024.
A straightforward numerical majority would keep the special arrangements in place for another four years.
Alternatively, if the arrangements get cross-community consent - in other words, if they're passed by most nationalists and most unionists - they would remain in place for eight years.
But a vote couldn't happen if the assembly wasn't operating.
Shortly afterwards, an election left unionism without a numerical majority in the Stormont chamber for the first time in the history of Northern Ireland.
So for the DUP, the issue of consent - and a fear that Dublin and Brussels would have too big an influence on trading rules - goes to the heart of the party's concerns that Northern Ireland's place in the UK would be weakened.
Several rounds of talks to restore the Stormont Executive haven't succeeded - and few, if any, hold out hope that devolution is returning in the coming weeks.
Her tweet - "No border and no veto" - shows how the complexities of Stormont politics have become increasingly bound up with the UK-EU negotiations.
The technical talk about Brexit and the border focuses on trade, goods regulations, and potential tariffs.
But for politicians in Belfast and Dublin, the significance of those issues is generated by deeper issues - such as identity, nationality, and peacebuilding.

Meetings, on their own, are not a Plan B. Conversations, are not by themselves, compromises.
To get any deal done where there are such clashing views all around, it requires give and take. It feels like a political lifetime since there has been a fundamental dispute in the cabinet, in the Tory party and across Parliament. Theresa May has stubbornly, although understandably, tried to plot a middle course.
But that has failed so spectacularly at this stage. Ultimately she may well be left with the same dilemma of which way to tack.
It's clear, wide open, in public, that the cabinet is at odds with each other. Just listen to David Gauke and Liam Fox on whether a customs union could be a compromise for example.
The answer for her is not suddenly going to emerge from a unified tier of her top team. There are perhaps five or six of the cabinet who would be happy to see that kind of relationship as a way to bring Labour on board.
But there is a group of around the same size who would rather see what they describe as a "managed no deal".
You may well wonder if that isn't a contradiction in terms.
But the principle would be that the UK would pay the divorce bill already agreed and over a two-year period construct a series of side deals on specific issues, rather than try to come up with a whole new comprehensive plan.
There are already intense arguments about whether that's remotely realistic. But the overall point is that the prime minister cannot just therefore look to her top colleagues for an immediate solution.
Before she decides which way to tack, or how far to budge, she may need to ask herself if the talks she wants to hold with other political parties are occasions when she is really open to ideas - or just ways of managing the political situation.
One cabinet minister involved in the talks suggested that many MPs still needed to understand how the agreement they have reached with the EU worked. And that as "project reality" dawned, there could still be a way through of salvaging Mrs May's deal in something like its current form.
And certainly there wasn't much in the PM's lectern statement to suggest she is suddenly ready to move very much. One former minister described it as "still flicking the V at the 48% - she's deluded, she never changes her mind and cannot conceive that others might".
If all that the prime minister intends to do is massage a few egos with these talks, it seems unlikely that she'll find a quick route to success. And Labour may well stay outside the process.
Many members of the public might be furious that Labour leader Jeremy Corbyn won't play nice during a time of crisis. He's always said he believes in dialogue, but when it really matters, he says no. But inside the Labour movement there are others who might accuse of him of helping to make Brexit happen if he takes part. Like so many facets of this process, it's not a straightforward political calculation.
But across Parliament, for a very long time now, even some MPs who were on the prime minister's side to start with have been intensely frustrated that she hasn't listened. It will take a lot more than a cup of tea in Downing Street to bring her many critics on board.

The UK and European Commission have reached an agreement that should allow them to move Brexit talks on to the next stage.
Here are some of the key lines in the agreement document.
So here's the first linguistic somersault. This agreement is designed to lock in the progress made so far, and allow technical experts to continue to work on it during the second phase of talks.
But EU negotiations always work on the principle that nothing is agreed until everything is agreed, and that raises the prospect that if the second phase runs into trouble, then what has been agreed so far could, in theory, unravel.
That is certainly not the intention on either side, but it underscores that the negotiating process still has a very long way to run - and the hardest part is still to come.
The separation agreement on citizens' rights will not fall under the direct jurisdiction of the European Court of Justice (officially called the CJEU but commonly referred to as the ECJ) which was the initial demand from the European Union.
But the ECJ will continue to play a role, because this agreement says UK courts will have to pay "due regard" to its decisions on an indefinite basis.
And for eight years after Brexit, there will be a mechanism for UK courts to refer questions of interpretation directly to the ECJ.
It is a compromise, but the sort of compromise that some supporters of Brexit will find hard to stomach.
This detail on citizens' rights is important.
The agreement will apply to anyone taking up residence before the UK leaves the EU, so people could still take the decision to move next year, or even in early 2019, and they would be fully protected by it. That option will remain open for new arrivals until the day the UK leaves - currently presumed to be 29 March 2019.
In fact the European Commission argues that the "specified date" should be considerably later. In an official communication to the European Council it argues that during a transition all EU citizens should have all their rights upheld. In other words, it says, the "specified date" should not be the actual date of withdrawal, but the final day of a transition period (potentially two years later or even longer).
There are also a lot of technical details hidden in the weeds of the agreement that remain to be negotiated, and that's why some groups representing citizens who are caught up in this dilemma are far from happy.
The reaction of the European Parliament, which has taken a tough line on citizens' rights, will be important because it has to ratify the final agreement.
This is the key phrase in the long section setting out how the border between Northern Ireland and the Republic of Ireland will operate after the UK leaves the EU.
The preference on both sides is for an ambitious free trade agreement, which will address many of the concerns that have been raised (although questions of customs duties would still have to be addressed).
As a backstop though, the UK has guaranteed that it will maintain "full alignment" with the EU's single market and customs rules that govern cross-border trade.
It is a form of words that everyone can (just about) live with for now, but there is plenty of tough negotiating ahead.
It's not entirely clear how full alignment could be maintained without Northern Ireland staying in the single market and the customs union, especially as there is no such thing as partial membership. It is another sign that the competing demands that have been discussed this week have been sidestepped, but not fully resolved.
This sentence about the financial settlement is a bureaucratic masterpiece, and suggests that plenty of detail still needs to be sorted out behind the scenes.
For months, the money appeared to be the most intractable issue in the withdrawal negotiations, but money is easier to finesse than borders or courts.
A method for calculating the bill has been agreed, but the calculation of an exact UK share will depend on exchange rates, on interest rates, on the number of financial commitments that never turn into payments, and more.
The question of how and when payments will be made still needs to resolved, but it will be a schedule lasting for many years to come, and it is highly unlikely that anyone will ever be able to give an exact figure for the size of the divorce bill.
UK sources say it will be up to £40bn, but some EU sources expect it to be higher than that. No-one can say for sure, and both sides want to keep it that way.
Update 11 December 2017: This piece was amended to take account of the European Commission's view on the specified date for EU citizens' rights.
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Tory rebels "could collapse the government" if they vote against a Brexit deal negotiated with the EU, a leading rebel has said.
Dominic Grieve said he wakes up "in a cold sweat" thinking about what could happen if a final deal is rejected.
But he suggested rebels would not back down in a current row with ministers about how much of a say MPs should get.
The EU Withdrawal Bill returns to the Lords and Commons this week, with further rebellions expected.
Last week the government avoided a defeat on the bill after agreeing to hold further talks with rebels.
They want a bigger role for Parliament, should a final Brexit deal be rejected by MPs, or if no deal is reached - the so-called "meaningful vote".
Former Attorney General Mr Grieve told BBC One's Sunday Politics that he thought they had agreed MPs could have an "advisory" vote, that would not order the government to do anything, but would help people to "keep calm" during what would be a "critical situation".
But after two days of talks, Mr Grieve said a government amendment drawn up to avert a rebellion was changed at the last minute and was now "valueless".
He implied rebels would vote against it this week: "I'm absolutely sure that the group is quite determined that the meaningful vote pledge, which was given to us, has got to be fulfilled."
He added: "The alternative is that we've all got to sign up to a slavery clause now, saying whatever the government does, when it comes to January, however potentially catastrophic it might be for my constituents and my country, I'm signing in blood now that I will follow over the edge of a cliff, and that I can tell you, I am not prepared to do."
The government's amendment to the EU (Withdrawal) Bill sets out what must happen in the event of three scenarios: If MPs vote down the UK-EU Brexit deal, if Theresa May announces before 21 January 2019 that no deal has been reached, or if 21st January passes with no deal being struck.
Under these circumstances, a minister must make a statement in Parliament setting out their next steps and give MPs an opportunity to vote.
However, the vote would be on "a motion in neutral terms", merely stating that the House has considered the statement.
Rebels had originally wanted the amendment to say that the government must seek the approval of Parliament for its course of action - and that ministers must be directed by MPs and peers.
When it was put to him that voting against any Brexit deal at "the 11th hour" of negotiations could cause the government to collapse, he replied:  "We could collapse the government and I can assure you, I wake up at 2am in a cold sweat thinking about the problems that we have put on our shoulders."
Last week another Conservative MP, Tom Tugendhat, told Sky News there was "going to be a new government" if MPs rejected the government's Brexit deal.
Solicitor General Robert Buckland said that "however well intentioned" Mr Grieve's plan had been, his worry was that "it actually plays badly in the most important negotiation, which is over in Brussels".
It would imply to the EU, he said, that "there's a third party in this relationship" - Parliament - which could "trump whatever the UK government say".
He said ministers would stick with the new amendment for Monday, adding: "Let's see what the Lords make of it. Of course we have Tuesday to consider matters ahead of the Wednesday vote."
Earlier the prime minister defended her handling of the row.
She told BBC One's Andrew Marr Show she had met Tory rebels and "undertook to consider their concerns".
She admitted there had been "a debate" about what a "meaningful" vote for Parliament meant: "I've listened carefully to the concerns, I've put an amendment down which I think balances this issue of the role of Parliament together with the need for us to ensure we don't overturn the decision of the British people."
But she said Parliament "cannot tie the hands of government in negotiations".
The main purposes of the EU Withdrawal Bill are to end the supremacy of EU law in the UK, and transfer existing EU law into UK law so the same rules and regulations apply on the day after Brexit.
But as it passes through Parliament, MPs and peers have been trying to change it, in some cases adding bits on that would change the government's Brexit strategy.
The government says the whole row is about a "hypothetical" scenario and they are "confident we will agree a good deal with the EU which Parliament will support".

As MPs begin five days of debate on Theresa May's Brexit deal it looks like the prime minister faces the exact situation she called an election last year to try and avoid.
Whether it is the decision on whether the government is in contempt of Parliament (in other words, in lots of embarrassing trouble for ignoring the demand to publish the full Brexit legal advice), or MPs asking for the right to tell ministers what to do if there is a second attempt by the government to get Theresa May's Brexit compromise deal through the Commons (the attempt by Dominic Grieve today, that could take 'no deal' off the table for good), or what seems now, the likely rejection of  Theresa May's agreement with the EU next week, those manoeuvres, those sub-plots in the Brexit drama, amount to one central thing - slowly but surely, Parliament grasping the levers of power - one might even say, taking back control.
To use the posh term, it is the legislature trying to take over the executive, and this is what chills some spines in No 10. With MPs on the Tory benches as well as the opposition looking for ever more arcane ways of tying ministers up in knots, there is a sense whatever happens next Tuesday, what we are seeing is the gumming up of the government, maybe for good.
For many MPs of course, this is a moment, if not to hang out the bunting, to take heart from Parliament's influence, to be reassured about its role, its ability not just to scrutinise legislation, but to make things happen, or more pertinently, to stop them taking place.
But remember, as one government insider put it this morning, "there are no numbers FOR anything" - in essence the idea that the Commons would be able to come together to agree anything quickly on behalf of the country seems optimistic in the extreme.
They'd be able to agree that they should prevent a disorderly 'no deal' exit. The prominent Labour MP, Hilary Benn, is making a formal attempt to guarantee just that.
But beyond that? If the government's plan falls, some MPs will certainly push for another referendum - but a majority for that seems out of reach for now. Some, and there is cross-party support, would try to argue for a Norway-style deal with close economic ties to the EU. There might, just about, be a majority for that.
But that model would not see the UK have total control of its immigration policy. For many, but of course not all, Leave voters, that was the priority in the referendum. It's potentially therefore deeply problematic to go for such an arrangement.
If voters partly voted Leave to demand more say over immigration, what message does Westminster send back to the electorate if they carve up a deal that simply does not do that?
Of course MPs absolutely ought to be voting for what they believe is best, at this huge moment. Some of them may be spooked by the idea of turmoil, or at least on-going confusion.
Many more are poised to make their objections count.
But don't kid yourself that if Parliament takes charge of the process that the situation will become any clearer fast.
By calling the election last year, this kind of Parliamentary mess was exactly what the prime minister was trying to avoid. She had a tiny majority then, and this would have been a hard fight in any case.
But that historic gamble, that she tried and failed, has made this perhaps harder than she could have imagined. With no majority, even tiny numbers of MPs can make a huge amount of noise.

The request for delay is an answer to one question.
When confronted with the possibility of taking the UK out of the EU without a formal deal in place or slamming on the brakes, which way would the prime minister jump?
Would she choose a pure plan - pursuing Brexit over the risk of instability?
Or would Theresa May heed the voices of warning, rather than those in her own party arguing that any short-term pain would be worth long-term gain, and ask for delay, despite the embarrassment of doing so, and the frustration of those who wanted her to keep the promise of leaving on time?
Mrs May kept many in Westminster guessing for a long time.
But her meetings in Europe, her plea on Tuesday, are evidence of the decision she finally took - that almost any entreaties to European leaders are worth it to avoid opening Pandora's Box. Pausing again brings embarrassment and angers many on her own side, but it's a lesser evil than departing with no deal.
If the prime minister is granted a strings-attached delay later, the next question is perhaps as big.
What will she do with the extra time she's been granted? Will it even be up to her?
Cross-party talks with the Labour Party are serious - both sides in the room are taking part in good faith and expect more negotiations on Thursday.
But the more talking they do, the more the scale of the task to bring them together reveals itself.
Forget a quick solution from this joint process, and don't bank on one happening at all.
The divisions may simply be too great - the moment when it might have worked perhaps has passed.
If that fails, then the answer may pass again, back to Parliament - MPs confronted again with the power to choose from a wide array of different choices - with the ability, if not yet the common purpose to choose a version of Brexit for all of us.
And of course, if a long delay is agreed it could push hungry Tories who want a change of leadership again into action.
But the obvious response to another question is crystal clear - who is in charge for today?
It's the EU leaders who will determine the date and nature of this delay - not the country that voted in an effort to pull back control.

The Brexit process has turned into a "nightmare", the prime minister of Luxembourg has said after holding talks with UK PM Boris Johnson.
Xavier Bettel said Mr Johnson had failed to put forward any serious plans to allow a deal by 31 October.
But Mr Johnson, who cancelled his press conference because of the noise from protesters, said "there's been a lot of work" and "papers have been shared".
He urged the EU to make "movement" in its opposition to scrap the backstop.
Mr Johnson said his joint press conference was cancelled over fears the two leaders would have been "drowned out" by pro-EU protesters.
"I don't think it would have been fair to the prime minister of Luxembourg," he said.
"I think there was clearly going to be a lot of noise and I think our points might have been drowned out."
Political editor Laura Kuenssberg said that Number 10 had asked for the press conference to be held inside, according to sources.
Mr Bettel, who conducted the planned press conference alone, said the "only solution" was the existing withdrawal agreement.
He said there were "no concrete proposals at the moment on the table" from the UK and said the EU "needs more than just words".
"We need written proposals and the time is ticking so stop speaking and act," he said.
"But we won't accept any agreement that goes against a single market, who will be against the Good Friday Agreement."
Away from the crowds, Mr Johnson said the EU must make "movement" in its opposition to scrap the Irish backstop, but insisted there was "just the right amount of time" to get a deal done.
When asked what concrete proposals he had made, Mr Johnson said "there's been a lot of work" and "papers have been shared".
"We've got to manage this carefully. Yes, we've got a good chance of a deal. Yes, I can see the shape of it. Everybody could see roughly what could be done," he said.
He reiterated that the UK will come out of the EU on 31 October "deal or no deal".
As soon as we arrived at the office of the prime minister of Luxembourg it became obvious a planned outdoor news conference could not go ahead.
The anti-Brexit protesters in the square numbered fewer than a hundred but their music and megaphones made it sound like a lot more and they occasionally used language you wouldn't want to hear on the news.
Behind the scenes the British and Luxembourgish delegations grappled with a diplomatic dilemma - move the event inside but exclude the majority of the journalists? Gamble that the demonstrators could pipe down for a bit? Silence the host to save the guest's blushes?
The end result saw Mr Johnson do a short interview at the ambassador's residence to be shared with everyone while Mr Bettel took to the stage next to an empty podium.
He used the moment in the spotlight to deliver an impassioned speech, made all the more dramatic by the fact he's famed as one of the EU's most smiley, mild-mannered leaders.
Earlier, both Mr Johnson and Mr Juncker - who met for the first time since the PM took office in July - agreed the discussions between the UK and EU "needed to intensify" and meetings "would soon take place on a daily basis".
But regardless of the outcome, No 10 said the PM would take the UK out of the EU on 31 October.
Downing Street also said Mr Johnson confirmed his commitment to the Good Friday Agreement - the peace deal brokered in Northern Ireland - and still had a "determination to reach a deal with the backstop removed, that UK parliamentarians could support".
Mr Johnson has called the Irish backstop "undemocratic" and said it needed to be removed from any deal with the EU.
A Downing Street spokesperson said Mr Johnson also reiterated he would not request an extension and would take the UK out of the EU on 31 October.
The EU has said it is willing to look at alternatives, but that an insurance policy like the backstop must be in place.
The backstop is the controversial policy in the existing withdrawal agreement, rejected three times by MPs, which would require the UK to follow the EU's customs rules to ensure there are no physical checks on the border between Northern Ireland and the Republic.
Last week MPs passed a law that would force the prime minister to ask the EU for an extension to the 31 October deadline if a deal was not agreed by 19 October.
But the prime minister's official spokesman said: "The position of the PM is that we comply with the law, but that we are leaving on 31 October whatever the outcome."
They also confirmed that the current date set for a transition period - the time for the UK and EU to negotiate their future relationship after officially leaving - of December 2020 would not be extended.
Over the weekend Mr Johnson told a newspaper that the UK would break out of its "manacles" like cartoon character The Incredible Hulk - with or without a deal.
The BBC's political editor Laura Kuenssberg said the issue of whether the UK had the legal right to leave on 31 October - come what may - could end up in court.
Reports have suggested Mr Johnson is considering a plan to keep Northern Ireland more closely aligned to the EU after Brexit, as an alternative to the current Irish backstop.
The Democratic Unionist Party - which supports the Conservatives in Parliament - has rejected any plan that would see Northern Ireland treated differently to the rest of the UK.
The PM's spokesman would not give details, but said the government had "put forward workable solutions in a number of areas".
Writing in Monday's Daily Telegraph, Mr Johnson said he believed he could strike a deal with the EU within weeks and was working "flat out to achieve one".
"If we can make enough progress in the next few days, I intend to go to that crucial summit... and finalise an agreement that will protect the interests of business and citizens on both sides of the channel, and on both sides of the border in Ireland," he wrote.
Many MPs have also questioned how serious the government is about getting a deal, such as former justice secretary David Gauke who said "detailed proposals" had yet to be put forward.
"It still remains the case the UK government has not produced detailed proposals as to how it wants to replace the Irish backstop," he told Radio 4's Today.
Foreign Secretary Dominic Raab said the PM would stress he wanted a deal, but there had to be "some finality" to it.
He said claims from the EU side that the UK was dragging its feet were part of the "tactical posturing that goes on in any negotiation".
He told Today the UK had been clear the "anti-democratic backstop" had to be removed from the current withdrawal agreement, and the outline of future trading relationship set out in the political declaration had to be much more ambitious.
"The EU knows our position. Lots of the detail has been talked through at technical and political level," he said. "The framework is very clear.
"But of course the nature of these negotiations is that there will be a tendency to rubbish things we put forward in order to exact further demands. We are not going to get involved in that."
Monday:  Boris Johnson meets European Commission President Jean-Claude Juncker for Brexit talks in Luxembourg
Tuesday: The Supreme Court begins to consider the legality of Mr Johnson's decision to suspend parliament until 14 October
Wednesday: The European Parliament to debate Brexit

Their offices are full of boxes, they're living in hotels and don't ask them when they're having their leaving drinks. How have the UK's MEPs been coping with the ever-changing Brexit situation?
It's the last day of the European Parliament in Strasbourg before the elections in May, but there's not much last-minute packing for the UK group of MEPs - they've been ready to go for nearly a month.
When the UK voted to leave the EU, the country's representatives in the European Parliament expected to be out of a job on 29 March. Instead they have watched two deadlines pass by as MPs in Westminster failed to agree on the withdrawal deal.
Now a new Brexit date of 31 October means the UK is likely to take part in European elections on 23 May and some MEPs are eyeing an unexpected return to Europe.
But job prospects there could be short-lived. Whenever the UK breaks the Brexit deadlock, they could be sent home. And if the prime minister succeeds in winning support for a deal before polling day, elections could be called off altogether.
MEPs are used to a nomadic life, dividing their time between parliament sessions in Brussels and Strasbourg, as well as their home constituencies in the UK. But many of them feel recent months have taken an already unstable situation to extremes.
Catherine Bearder, Liberal Democrat MEP, says: "Life is never certain as a politician, but this is beyond anything I've ever seen before."
The 70-year-old had been planning a quiet retirement - "painting, gardening, doing yoga" - but said she is back on an election footing now, determined to fight to keep the UK's place at the European table.
For Nathan Gill, a former UKIP and independent MEP who has now joined the newly launched Brexit Party, the delays have been a blow to the cause he spent the last 15 years of his life on.
Speaking from an office filled with packing boxes, he says: "It's unbelievable, it's disgraceful."
He says he was forced to leave his Brussels apartment and move into a hotel after his lease ended. Later he got turfed out of there too.
As UK Prime Minister Theresa May sought the latest extension to Brexit and an emergency EU summit rolled into town, prices rose so much that Mr Gill had to temporarily decamp to Antwerp, some 25 miles (41km) away.
Every country in the EU elects representatives to the parliament, which meets in Strasbourg and Brussels. The UK has 73 MEPs, representing each of its 12 regions for five-year terms.
Their job is to debate and to help decide on EU laws, as well as scrutinising the work of EU institutions.
The last election saw 19 Conservatives elected, 20 from Labour and 24 from UKIP - although 19 UKIP MEPs have since left the party and one was expelled.
The Greens have three MEPs, the SNP has two and there is one each from the Liberal Democrats, Democratic Unionist Party, Sinn Fein, the Ulster Unionist Party and Plaid Cymru.
Labour's David Martin is the UK's longest-serving MEP, first elected in 1984.
The Brexit Party is not the only new party planning to contest these European elections. Change UK - formed by former Labour and Tory MPs, initially under the name The Independent Group - says it had 3,700 people applying to be candidates.
MEPs themselves will receive a transitional allowance when their term ends, equivalent to a month's salary for every year they have served. But across the political spectrum, they are united in feeling that staff have been treated badly.
Each MEP has a budget to hire assistants, with up to three in Brussels as well as staff in their home region. Information about the future for these staff members is scarce and always changing, MEPs say.
Contracts could not be extended until Brexit extensions were officially confirmed by the European Council, usually at the last minute as negotiations went to the wire.
For some staff, the last-minute deadline extensions meant losing redundancy pay as they had already accepted jobs elsewhere. Others who remain are sleeping on sofas as their apartment leases run out.
"It's very brutal from a staff point of view," says Conservative MEP Daniel Dalton. "You're in one day and out the other and your staff are out with you."
Green MEP Jean Lambert says staff had to be made redundant and offices closed as the original Brexit deadline loomed in March. But the party kept in place a contingency plan in case the UK took part in European elections.
"We've got a plan A and a plan B, which is more than the government has," she says - although she plans to retire as an elected representative.
If the UK does elect MEPs, what will they do in a potentially short-lived return to Brussels and Strasbourg?
Some Brexiteer politicians such as Nathan Gill warn that they plan to make the EU nations "regret" the UK MEPs' return.
Mr Gill says the Brexit Party hopes to work with other anti-EU and anti-euro parties across the continent, such as the far-right Alternative for Germany (AfD) and Italy's anti-immigration League party, to cause disruption.
"We want them to realise they should have just let us go," he says. "They don't need this thorn in their side."
But Conservative MEP Mr Dalton, who backs the government's Brexit withdrawal agreement, says it would be "completely counter-productive".
He says British politicians have often failed to understand that the EU Parliament is based on compromise, so the adversarial politics of Westminster fall flat. "All it does is annoy people," he says. "They're much more likely to get more stubborn."
UKIP MEP Stuart Agnew is another who has postponed retirement to take part in the elections, if they happen. He says he was surprised that Westminster MPs had let the Brexit deadlock get to this point.
"I would have lost a bet. I thought they would have banged heads together, that the Conservatives wouldn't want European elections and neither would Labour. I was wrong," he says.
Other MEPs have made firm decisions not to stand again but have still been left bewildered by recent weeks.
David Martin, Labour MEP, says he intends to do academic lecturing on the EU and trade policy, but had been struggling to agree a start date.
"The Brexit negotiations will be a really good case study in how not to negotiate with the European Union," he says.
He has also been puzzling over a unique issue of etiquette: when should Brexiting MEPs say their goodbyes?
As Mr Martin puts it: "You don't want to have a farewell dinner and say goodbye to everyone, and still be there the next day."

Hundreds of thousands of people have marched in central London calling for another EU referendum, as MPs search for a way out of the Brexit impasse.
Organisers of the "Put It To The People" campaign say more than a million people joined the march before rallying in front of Parliament.
Protesters carrying EU flags and placards called for any Brexit deal be put to another public vote.
On Thursday, European leaders agreed to delay the UK's departure from the EU.
PM Theresa May is coming under pressure to quit after saying she might not put her Brexit deal to a third vote by MPs.
Speakers at the rally included Labour's deputy leader Tom Watson, Scotland's First Minister Nicola Sturgeon, London Mayor Sadiq Khan, former Tory turned independent MP Anna Soubry and former attorney general Dominic Grieve.
Crowds were told the initial count showed more than a million people had turned up - putting it on a par with the biggest march of the century, the Stop the War march in 2003.
There was no independent verification of the numbers but BBC correspondent Richard Lister, who was at the scene, said it was a "very densely packed" protest and people were still arriving in Parliament Square five hours after the march began.
He said: "The organisers say it was one million-strong, it's very hard to verify those kinds of claims but this was a very significant march, well into the hundreds of thousands."
Labour's Tom Watson told the crowd in Parliament Square that Mrs May's deal was a "lousy" one - whether you voted Leave or Remain.
He said he had this message for her: "I can only vote for a deal if you let the people vote on it too. Prime Minister, you've lost control of this process, you're plunging the country into chaos, let the people take control."
Ms Sturgeon said now was "the moment of maximum opportunity" to avoid a no-deal Brexit.
By Katie Wright, BBC News, in Park Lane
The streets around Park Lane were teeming with people hours ahead of the march's scheduled 1pm start, having come from all corners of the country - and some from further beyond.
The blue and yellow of the EU was splashed all over the ever-expanding crowd, which was full of groups of families, friends, colleagues and political groups.
Many people came draped in flags and carried homemade signs, featuring slogans ranging from playful - "Never gonna give EU up" - to political - "Forget the Ides of March - beware the Brexit of May". And then there were the plain angry - "Brexit is treason".
One member of the crowd, German-born vet Chris Reichmann, described it as a "carnival" atmosphere - with "lots of different nationalities" but "really British in a way".
And it was noisy, with some of London's most recognisable streets overflowing with people marching steadily to a soundtrack of beating drums, whistles and blaring horns.
Occasionally the hordes would erupt into spontaneous cheering, as well as chants of "What do we want? People's vote. When do we want it? Now!"
Game Of Thrones star Lena Headey, Strictly Come Dancing presenter Claudia Winkleman and Neil Tennant of the Pet Shop Boys were among the famous names to take to the streets.
Sadiq Khan joined demonstrators at the front of the march as it began, holding up a "Put it to the People" banner.
He was flanked by Liberal Democrat leader Vince Cable, who tweeted that there was a "huge turnout of people here from all walks of life".
But veteran Conservative MP John Redwood told the BBC: "We know that 16 million people wanted to stay in the EU, and some of those would still like to stay in the EU, and within that quite a few would like to have another go and have another referendum - but it was always a minority."
The prime minister wrote to all MPs on Friday saying she will ditch plans to put the deal to another so-called meaningful vote on her withdrawal deal if not enough MPs support it.
Unless her deal is passed by MPs, the UK will have to come up with an alternative plan or else face leaving without a deal on 12 April.
Downing Street sources have denied reports in the Times newspaper that discussions are under way about a timetable for the prime minister to step down.
Meanwhile, a record-breaking online petition on Parliament's website calling for Brexit to be cancelled by revoking Article 50 has attracted more than four million signatures.
As the number of signatures on the petition continued to climb, its creator Margaret Georgiadou said she had "received three death threats over the phone", and a "torrent of abuse" via her Facebook account.
Liberal Democrat MP Layla Moran said the petition could "give oxygen" to the campaign for another Brexit referendum.
The march comes as the pro-Brexit March to Leave, which started in Sunderland a week ago, continues towards London.
Former Ukip leader Nigel Farage re-joined the March to Leave in Linby, near Nottingham, on Saturday morning telling around 200 Brexit supporters that Mrs May had reduced the nation "to a state of humiliation".
Speaking from the top of an open-top bus, Mr Farage said those gathering for the People's Vote march in London were not the majority, before leading the marchers through the village.

Sir Vince Cable - the likely next Lib Dem leader - says he is "beginning to think Brexit may never happen".
He said "enormous" divisions in the Labour and the Tory parties and a "deteriorating" economy would make people think again.
"People will realise that we didn't vote to be poorer, and I think the whole question of continued membership will once again arise," he said.
He was speaking on the BBC's Andrew Marr show.
His comments were dismissed by leading Eurosceptic Conservative MP Owen Paterson, who said Sir Vince was just "chucking buckets of water around" and ignoring the "huge vote" in favour of leaving in the referendum and at the general election, where the two main parties backed Brexit.
"Vince Cable's party went down in votes, as did the other little parties who want to stay in the European Union," he told the BBC's Sunday Politics.
He added: "I am afraid Vince is behind history. We are going to leave. We are on target."
Sir Vince conceded that the Lib Dem policy on a second referendum on the terms of a Brexit deal "didn't really cut through in the general election".
But he said it could offer voters "a way out when it becomes clear the Brexit is potentially disastrous".
The former business secretary looks set to be crowned Lib Dem leader. He is the only candidate following the resignation of Tim Farron.
Sir Vince told the BBC he wants to work with Labour and Tory MPs to block what he regards as Theresa May's "hard Brexit" policy.
"A lot of people are keeping their heads down," he said, and "we'll see what happens" when MPs returned from their summer break.
But he added: "I'm beginning to think that Brexit may never happen.
"The problems are so enormous, the divisions within the two major parties are so enormous. I can see a scenario in which this doesn't happen."
MPs are set to vote on the Repeal Bill, a key piece of Brexit legislation, in the autumn.
Sir Vince has said he wants to form a cross-party coalition including like-minded Tory and Labour MPs to oppose Britain's exit from the single market - the official policy of both the Conservative and Labour parties.
He said Labour MPs who disagreed with their leader's position were welcome in his party, and predicted Labour's divisions on the issue would get worse.
"Jeremy Corbyn had a good election, for sure, but there is an element of a 'bubble' about it," he told Andrew Marr.
"He managed to attract large numbers of people on the basis that he was leading opposition to Brexit.
"Actually he is very pro-Brexit, and hard Brexit, and I think when that becomes apparent, the divisions in the Labour Party will become more real and the opportunity for us to move into that space will be substantial."
Sir Vince has come under fire for saying Theresa May's comment, in her 2016 Conservative Party conference speech, that "if you believe you're a citizen of the world, you're a citizen of nowhere," was like something out of Adolf Hitler's Mein Kampf.
Quizzed by Andrew Marr on this, Sir Vince said he had got the wrong dictator: "I got my literary reference wrong - I think it was Stalin who talked about 'rootless cosmopolitans'."
Sir Vince, who won back his Twickenham seat at the general election, is not expected to face a challenger for the Lib Dem leadership but he said would still produce a manifesto. He suggested he would back income tax rises to pay for improvements to health and social care.

Donald Tusk has insisted the EU "does not want to build a wall", but Brexit means "we will be drifting apart".
The EU Council president said Theresa May wanted to "demonstrate at any price that Brexit could be a success", but that was not the EU's objective.
He was unveiling draft guidelines for the EU side of Brexit trade talks.
Mr Tusk said the EU wanted an "ambitious and advanced" free trade deal - and continued access to UK waters for EU fishing vessels.
"Our agreement will not make trade between the UK and EU frictionless or smoother," he said.
"It will make it more complicated and costly than today for all of us. This is the essence of Brexit."
He said it would be the first time in history that a free trade agreement would "loosen, not strengthen, economic ties".
The draft European Council guidelines call for zero-tariff trade in goods - where the EU has a surplus.
The document also says access for services will be limited by the fact that the UK will be outside the EU and will no longer share a common regulatory and judiciary framework.
The draft guidelines repeat EU warnings that there can be "no cherry-picking" of participation in the single market for particular sectors of industry.
The BBC's Reality Check correspondent Chris Morris said the "narrow negotiating mandate set out in these guidelines suggests that the EU doesn't think it will be much more ambitious than other free trade agreements it has negotiated - Canada is the most obvious example".
Mr Tusk said he wanted continued security and research cooperation and to ensure flights were not grounded.
But he added: "No member state is free to pick only those sectors of the internal market they like, or to accept the role of the ECJ only when it suits their interest."
The draft guidelines also say that the EU will "preserve its autonomy as regards its decision-making, which excludes participation of the United Kingdom as a third-country to EU Institutions, agencies or bodies".
Mrs May acknowledged in her Mansion House speech on Brexit on Friday that neither side would get everything they want from negotiations.
But she also stressed that the UK wanted a bespoke trade deal, rather than an "off-the-shelf" model.
"The fact is that every free trade agreement has varying market access depending on the respective interests of the countries involved," she said.
"If this is cherry-picking, then every trade arrangement is cherry-picking."
She also said: "We will also want to explore with the EU, the terms on which the UK could remain part of EU agencies."
This appears to be in conflict with the EU draft guidelines, although BBC Research has found several examples of non-EU members participating - as a member or observer - in EU agencies and bodies, such as the European Environment Agency and the European Medicines Agency.
The EU says it wants to maintain "existing reciprocal access to fishing waters" - a leading concern of the fishing industry in countries bordering the North Sea.
In her Mansion House speech, Mrs May said: "The UK will regain control over our domestic fisheries management rules and access to our waters."
She added that the UK would want to "work together to manage shared stocks in a sustainable way and to agree reciprocal access to waters and a fairer allocation of fishing opportunities for the UK fishing industry".
Brexit Secretary David Davis - quizzed on Tuesday by Brexiteer Labour MP Kate Hoey - insisted the government would not betray UK fishing communities by "trading away fishing rights" for "other things".
Asked about the EU's demand to keep access as it is now, Chancellor Philip Hammond said the UK was "open to discussing with our EU partners about the appropriate arrangements for reciprocal access for our fishermen to EU waters and for EU fishermen to our waters".
Campaign group Fishing for Leave urged the government not to "cave in" to the EU demands, saying: "Nowhere else is access to fisheries included as negotiating collateral for a free trade agreement."
Financial services are not mentioned specifically in the EU draft guidelines, but it is shaping up to be a major sticking point.
UK Chancellor Philip Hammond has told European leaders that it is in the "mutual interest" of both the UK and the EU to include financial services in a free trade agreement.
"Given the shape of the British economy and our trade balance with the EU 27, it's hard to see how any deal that did not include services could look like a fair and balanced settlement," he said in a speech.
"Not only is it possible to include financial services in a trade deal, but this is very much in our mutual interest to do so."
But Donald Tusk appeared to reject the UK proposals. The EU says the UK will be treated like any other "third country" after Brexit.
Asked about the EU guidelines, which also warn of the "negative economic consequences" of Brexit, Mr Hammond said: "It does not surprise me remotely that what they have set out this morning is a very tough position. That's what any competent, skilled and experienced negotiator would do."
EU deal 'must include financial services'
Donald Tusk unveiled his guidelines in a picture-perfect castle in the hills outside Luxembourg.
A nice change to the usual venues in Brussels but the same tough message from the EU that the UK's red lines limit what it can get from the final Brexit deal.
The best that's on offer is a free trade agreement on goods with no tariffs, and access to the European markets for the UK service sector - but under EU rules and with no specific mention of financial services.
I asked a sad-sounding Donald Tusk if his offer came anywhere close to what the prime minister had asked for in her Mansion House speech. His pause was epically long, which suggested he knows it is not.
His document is also pretty gloomy, with a spine-chilling warning about the economic costs to the UK.
But there is also a big offer tucked away in a later paragraph - there are other options available if the government is prepared to compromise on its red lines.
The leaders of the remaining 27 EU states must approve the plans at a Brussels summit on 22 March, setting the template for chief negotiator Michel Barnier for talks with the UK about their future relationship.
The UK is due to leave the EU at the end of March 2019, and both sides have said they would like a deal on their future relationship to be agreed by this autumn to allow time for parliaments to approve the deal before Brexit happens.
The European Parliament has stressed that its preferred option is for the UK to continue to be a member of the single market and customs union after Brexit, in a draft resolution, leaked to the Politico website.
The parliament does not have a formal role in the Brexit negotiations but does have a veto on the final deal.
The European Parliament document, which may be changed before it is adopted, says non-EU members - even if very closely aligned to the bloc - cannot expect the same rights and benefits as EU members.
It also warns that the UK's current "red lines" in Brexit talks "would lead to customs checks and verification which would affect global supply chains and manufacturing processes, even if tariff barriers can be avoided".
It says a "deep and comprehensive" trade deal, of the kind envisioned by Theresa May, must entail "a binding interpretation role" for the European Court of Justice.
MPs in Westminster are, meanwhile, debating a call by Plaid Cymru - who have four MPs in Wales - for UK nationals to be allowed to keep their EU citizenship after Brexit.
Plaid said EU citizenship would give holders the right to travel, live, study and work anywhere in the EU even after the UK leaves next year.
A UK government spokesman said only citizens of EU member states could hold EU citizenship.

A Brexit minister has apologised in Parliament for comments he made about the independence of the civil service.
Steve Baker said he had been told Treasury officials were deliberately trying to influence policy in favour of staying in the EU customs union.
Charles Grant, an EU policy expert said to have been the source of the claims, has since denied telling Mr Baker this.
Mr Baker told MPs he now accepted this and insisted that he had the "highest regard" for the civil service.
In a short speech in the Commons before proceedings began on Friday, Mr Baker said he wanted to set the record straight.
"As I explained yesterday (Thursday) I considered what I understood to be the suggestion being put to me as implausible because of the long standing and well regarded impartiality of the civil service," he said.
After Mr Baker's claims emerged on Thursday, Mr Grant, the Centre for European Reform think tank chief, issued a statement.
He said he recalled telling the minister at an event at the Conservative Party conference that he was aware of Treasury research showing the economic costs of leaving the customs union outweighed the benefits of striking free trade deals.
But he added: "I did not say or imply that the Treasury had deliberately developed a model to show that all non-customs union options were bad, with the intention to influence policy."
An audio recording of Mr Grant's lunch at the Tory conference has since been published online.
In his apology, Mr Baker said: "In the context of that audio I accept that I should have corrected or dismissed the premise of my Hon Friend's question.
"I have apologised to Charles Grant who is an honest and trustworthy man.
"As I have put on record many times I have the highest regard for our hard-working civil servants. I am grateful for this early opportunity to correct the record, and I apologise to the House."
Downing Street said it was "the right thing to do" for Mr Baker to have made a "heartfelt" apology for his comments, adding: "We consider this matter closed."
Theresa May's spokesman said the prime minister had not personally spoken to Mr Baker about the row but No 10 officials did have a word with him after the recording of Mr Grant's lunch emerged.
The row was sparked by Commons exchanges on Thursday at Brexit questions.
Prominent Brexiteer Jacob Rees-Mogg asked Mr Baker to confirm if he had heard Mr Grant that "officials in the Treasury have deliberately developed a model to show that all options other than staying in the customs union were bad and that officials intended to use this to influence policy".
In response, Mr Baker said he was "sorry to say" that Mr Rees-Mogg's account was "essentially correct", adding: "At the time I considered it implausible because my direct experience is that civil servants are extraordinarily careful to uphold the impartiality of the civil service."
Mr Baker, a leading backbench Eurosceptic before his promotion to a ministerial post, was challenged by opposition MPs as he delivered his answer to Mr Rees-Mogg, prompting him to add: "I didn't say it was correct. I said the account that was put to me is correct.
"It was put to me, I considered it an extraordinary allegation, I still consider it an extraordinary allegation."
Following Mr Baker's apology, Mr Rees-Mogg is continuing to insist that the Treasury has questions to answer over its stance on the customs union.
Theresa May has ruled out staying in the customs union - which allows tariff-free trade between its members but prevents them from negotiating their own trade deals - but has not excluded the possibility of some form of customs partnership with the EU after Brexit.

The Brexit vote must not be frustrated and the government needs to maintain an "absolute" focus on delivering it, Theresa May has said.
In a speech to Tory activists the PM said, as her negotiations with the EU reach their final stages, the "worst thing we could do is lose our focus".
It came as three pro-EU cabinet members warned they could vote to delay Brexit to prevent a "disastrous" no-deal.
But Mrs May said there must be no party "purges" over MPs with differing views.
Ahead of crucial votes in the Commons next week, Greg Clark, Amber Rudd and David Gauke told the Daily Mail they would be prepared to defy the prime minister and vote for a delay.
The intervention led to calls for their resignations by Tory Brexiteers.
The UK remains on course to leave the European Union on 29 March.
However, the government has repeatedly refused to rule out the possibility of the UK leaving without a formal deal, in the event that Mrs May cannot get MPs to approve the deal she negotiated with Brussels in time.
Mrs May's speech to the National Conservative Convention in Oxford on Saturday evening came as MPs prepare for a series of votes on Wednesday which could see Parliament take control of the Brexit process.
Delegates at the convention overwhelmingly backed a symbolic motion saying Brexit should not be delayed, and leaving without an agreement should remain an option.
Mr Clark, the business secretary, along with Ms Rudd, the work and pensions secretary, and the justice secretary, Mr Gauke, had earlier said they would be prepared to defy Mrs May and vote for a delay to Brexit.
They argued there  "simply will not be time to agree a deal and complete all the necessary legislation" unless a deal is approved in the coming days.
An amendment tabled by former Tory minister Sir Oliver Letwin and Labour's Yvette Cooper would give Parliament the opportunity to delay Brexit and prevent a no-deal situation if there is no agreement with the EU by the middle of March.
But Mrs May told activists: "Our focus to deliver Brexit must be absolute.
"We must not, and I will not, frustrate what was the largest democratic exercise in this country's history. In the very final stages of this process, the worst thing we could do is lose our focus."
Mrs May also said there should be no moves to deselect MPs because of their views on Brexit.
The resignations of three pro-Remain Tory MPs - Anna Soubry, Heidi Allen and Sarah Wollaston - to join a group of Labour defectors in the new Independent Group reduced the Tories working majority in Parliament to eight.
Mrs May said: "No-one gets more frustrated than I do when people vote against the whip, particularly given the tight Parliamentary arithmetic that we face.
"But we are not a party of purges and retribution. We called a referendum and let people express their views - so we should not be seeking to deselect any of our MPs because of their views on Brexit.
"Our party is rightly a broad church - on that and other issues."
Mrs May is expected to hold talks with European Council president Donald Tusk and other key EU figures in Egypt later during a summit between leaders of EU and Arab league countries.
But Downing Street has played down hopes of a breakthrough on her Brexit deal being reached in Sharm el- Sheikh.
The summit is the first between leaders of EU and Arab league countries and will focus on tackling concerns over security and migration, and boosting trade.

Some of the biggest names in science are pleading for a deal on Brexit to avoid damaging British and European research.
A letter to Theresa May and Jean-Claude-Juncker has been signed by 29 Nobel Laureates and six winners of the prestigious Fields medal.
Science needs "the flow of people and ideas across borders", it says.
It comes as a survey found that many scientists are considering leaving the UK.
Sir Paul Nurse, one of the signatories and a Nobel prize-winner for research into breast cancer, said: "The message is, 'take science seriously'."
Science can help tackle global challenges like treating disease, generating clean energy and guaranteeing food supplies, the letter says - but to do that it needs to bring together the most talented researchers.
And it says Britain and the EU "must now strive to ensure that as little harm as possible is done to research".
Funding and freedom of movement are the two big concerns.
Over the years of Britain's membership of the EU, leading scientists say that the UK has been extremely successful at landing European grants.
Britain's overall financial contributions have been larger than the sums received but the UK's top scientific academy, the Royal Society, calculates that British science as a sector has gained financially.
"...it receives a greater amount of EU funding for research and development than the proportion of its contribution analyses suggests is earmarked for this," it says.
Members states pay their national contributions into a central pot which is then divided between the different spending programmes.
The UK Office of National Statistics (ONS) reports an "indicative" figure for the UK's contribution to EU research and development of €5.4bn over the period 2007-2013.
During this time, it says, the UK received €8.8bn in direct EU funding for research, development and innovation activities.
Sir Paul reckons that without a deal, British science could lose about £1bn a year.
There had been hopes that Britain could rapidly negotiate a new science relationship with the EU, with an associate status like that of Switzerland, in which contributions are made and grants received. But that has not happened so far.
The other worry is that without freedom of movement, the brightest scientific talent may be put off by the bureaucracy of having to apply for a visa.
In an internal survey, staff at the Francis Crick Institute in London were asked for their views on Brexit - the Crick is the largest biomedical research centre under one roof in Europe.
Of the roughly 1,000 scientists on the staff, 40% are from EU countries and a priority was to find out what they might do after Brexit.
78% of the EU scientists said they were "less likely" to stay in the UK.
51% of all the institute's scientists - including those from Britain - said they were less likely to stay.
45% of lab heads said Brexit had already affected their work - either recruiting new scientists, being excluded from EU programmes or facing increased costs after the fall in the pound.
97% of those who responded said a no-deal Brexit would be bad for UK science.
One manager of a lab at the institute, Val Maciulyte from Lithuania, told me the "uncertainty" of the Brexit process meant she was considering moving after seven years in Britain.
"I think that definitely makes me think of other places than the UK, I'm thinking about other options in Europe, in central Europe, or even maybe going back to Lithuania," she said.
Jasmin Zohren, a post-doctoral researcher from Germany, said it was difficult to plan because "no one knows what is going to happen" but she wants to live in a country that is in the EU, despite "loving London".
She said: "I'm currently funded by the EU - also for my PhD which I did in the UK - and I know that lots of this money will not arrive in the UK any more. And of course that's a big concern."
A senior scientist, Monica Rodrigo from Spain, said that the uncertainty was having an impact on everyone.
"I think the biggest thing is the level of stress that people are having because it's not only affecting your professional life but it's affecting other things," she said.
"Even if you're a British scientist it's affecting how you carry on your life and what you're going to do in the future - are you going to stay where there's limited funding or go somewhere else?"
I put it to Sir Paul that even without a deal, British science would be strong enough to cope.
"We will of course survive, we will of course receive funding from the government and we will keep going," he says.
"But at the moment Britain is at the top of the tree; we are considered widely around the world to be the best and we are in danger of losing that top position if we don't get this right."
A government spokesman said: "The UK plays a vital role in making Europe a pioneering base for research, and values the contribution that international researchers make to the UK.
"This will not change when we leave the EU.
"We will seek an ambitious relationship on science and innovation with our EU partners, exploring future UK participation in mutually beneficial research programmes, and will continue to support science, research and innovation through our modern industrial strategy.
 "We have a proud record of welcoming the world's brightest scientists and researchers to work and study here, and after we leave the EU we will have an immigration system to support this."

The UK's Brexit negotiations have not begun well amid "differences" inside the cabinet, a former head of the diplomatic service has said.
Sir Simon Fraser, chief mandarin at the Foreign Office until 2015, said the UK side had been "a bit absent" from formal negotiations in Brussels.
Sir Simon, who now advises businesses on Brexit, said he was concerned the UK had not put forward a clear position.
Downing Street said it disagreed strongly with his comments.
The government is expected to publish "position papers" on key issues soon.
Speaking to BBC Radio 4's Westminster Hour, Sir Simon, who campaigned for Remain ahead of last year's referendum, said he feared divisions within the cabinet were preventing the government from presenting a united front.
"The negotiations have only just begun, I don't think they have begun particularly promisingly, frankly, on the British side," he said.
"We haven't put forward a lot because, as we know, there are differences within the cabinet about the sort of Brexit that we are heading for and until those differences are further resolved I think it's very difficult for us to have a clear position."
He added: "I think so far we haven't put much on the table apart from something on the status of nationals, so we are a bit absent from the formal negotiation."
He called on the government to publish further details about its views on issues, including future customs arrangements and the Northern Irish border in the coming weeks.
"I think we need to demonstrate that we are ready to engage on the substance so that people can understand what is really at stake here and what the options are."
Downing Street rejected Sir Simon's analysis.
"The last two months, we have had a constructive start to the negotiations. We have covered a significant amount of important ground," the prime minister's spokesman said.
"As the secretary of state for exiting the European Union said at the end of the last negotiating round, important progress has been made in understanding one another's positions on key issues."
Last month, Brexit Secretary David Davis said he was confident negotiations would continue as planned after reports Brussels may delay trade talks because of a lack of progress on the "divorce" settlement.
At the weekend, the Sunday Telegraph claimed UK negotiators are now prepared to pay up to £36bn to the EU to settle the so-called Brexit divorce bill.
Downing Street said it did not recognise this figure.
Conservative MP Peter Bone said it would be "totally bizarre" for the UK to give the EU any money, let alone £36bn, adding that such a fee was unlikely to get through Parliament.
Another Eurosceptic MP, Jacob Rees-Mogg, said there was "no logic" to the figure that was being reported.
Responding to Sir Simon's comments, Liberal Democrat Brexit spokesman Tom Brake said: "This government is in the middle of the single biggest economic and diplomatic negotiation in our history.
"Yet while the clock is running down, key cabinet members are still squabbling over what type of Brexit to pursue."
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The EU's chief negotiator said there would be "substantial" consequences from Brexit after the first round of talks with the UK.
Michel Barnier said he was "not in the frame of mind to make concessions or ask for concessions".
UK Brexit Secretary David Davis said talks got off to a "promising start".
The UK appears to have conceded to the EU's preferred order for the talks which will mean trade negotiations do not begin immediately.
Mr Davis and Mr Barnier gave a joint press conference after day one of the talks in Brussels.
The initial focus will be on expat rights, a financial settlement and "other separation issues".
Discussions aimed at preserving the Good Friday Agreement and common travel area in Ireland will also begin, although Mr Davis suggested these issues may not be settled until the end of the process, when the UK's trade relationship with the EU is settled.
The UK had wanted talks on its future relationship with the EU to be considered from the outset, but Mr Barnier said this would only happen once the European Council decided "sufficient progress has been made" on the other issues.
Mr Davis - who had predicted this would be the "row of the summer" - denied suggestions the agreed timetable showed Britain's "weakness" and insisted it was "completely consistent" with the government's aim of parallel trade and exit talks.
"It's not when it starts it's how it finishes that matters," he said.
Asked whether he had made any concessions to the UK in return, Mr Barnier said the UK had decided to leave the EU - not the other way around, and each side had to "assume our responsibility and the consequences of our decisions".
"I am not in a frame of mind to make concessions, or ask for concessions," he said.
"It's not about punishment, it is not about revenge.
"Basically, we are implementing the decision taken by the United Kingdom to leave the European Union, and unravel 43 years of patiently-built relations.
"I will do all I can to put emotion to one side and stick to the facts, the figures, and the legal basis, and work with the United Kingdom to find an agreement in that frame of mind."
Laura Kuennsberg, BBC political editor
It's often compared to a divorce - the UK wanted to talk about who gets the house and the CD collection at the same time as settling who pays for the kids' weddings in 20 years' time.
The EU on the other hand have been firm all along that the future arrangements could only be discussed once the terms of the initial split have been agreed.
The debate was called "parallelism versus sequentialism" and from this afternoon's press conference and the announcement of the procedure it is clear that the UK has lost.
Ministers believed they would be able to persuade the EU - the failure to do so has been described as a "total cave-in".
The discussion was even predicted by Mr Davis as likely to be the "row of the summer". The row won't happen because it seems the UK has already given in.
Mr Barnier said a "fair deal" was possible "and far better than no deal". He promised to work with, not against, the UK.
"We must lift the uncertainty caused by Brexit," he said.
The two men - who exchanged gifts at the start of the talks - set out the structure for the initial negotiations. There will be one week of negotiations every month.
Working groups of "senior experts" will be set up to focus on the three main areas.
On citizens' rights, which the UK has said should be an immediate priority, Mr Davis said there was "much common ground".
The UK is set to leave the EU by the end of March 2019, following last year's referendum vote.
Prior to the start of talks, Mr Davis gave his counterpart a first edition of a mountaineering book - a French-language version of Regards vers Annapurna - while Mr Barnier reciprocated with a traditional, hand-carved walking stick from Savoie, complete with leather wrist strap.
Who's who in the UK delegation?
After holding talks with Theresa May in Downing Street, new Irish prime minister Leo Varadkar said there must be no return to a hard border between Northern Ireland and the Republic of Ireland and economic borders must be "invisible".
While he said he regretted Mrs May's decision to leave the single market and customs union, he said the two had a shared objective to minimise disruption to trade after the UK's exit.
Earlier former Marks and Spencer chairman Lord Rose, who chaired the Stronger In campaign last year, told BBC Radio 4's Today programme that he was reassured that economic considerations were "top of the pile" but ministers needed to be realistic with the public.
Speaking on the same programme, JD Wetherspoon founder Tim Martin - one of the leading pro-Leave business voices - said negotiators had to be open to possible compromises but also prepared to walk away and to default to World Trade Organization rules if necessary.
"I don't think many people feel that staying in the single market and customs union and being subject to EU laws is Brexit.
"I think Brexit is parliamentary sovereignty and an assertion of democracy. Outside that, I think there is a quite a lot of scope," Mr Martin said.
For Labour, shadow Brexit secretary Sir Keir Starmer said there was "real confusion" about the government's mandate after the general election result.

The UK's offer on Brexit must be acceptable to the Republic of Ireland before the negotiations can move on, the president of the European Council, Donald Tusk, has said.
Mr Tusk was speaking after talks with the Irish prime minister in Dublin on Friday.
He said: "The UK's future lies - in some ways - in Dublin".
The European Union has said "sufficient progress" must be made on the Irish border before negotiations can move on.
"The Irish request is the EU's request," Mr Tusk said.
"I realise that for some British politicians this may be hard to understand.
"But such is the logic behind the fact that Ireland is the EU member while the UK is leaving.
"This is why the key to the UK's future lies - in some ways - in Dublin, at least as long as Brexit negotiations continue."
In a press conference with Taoiseach (Irish prime minister) Leo Varadkar, Mr Tusk said that the UK's decision to leave the EU had created "uncertainty for millions of people".
"The border between Ireland and Northern Ireland is no longer a symbol of division, it is a symbol of cooperation and we cannot allow Brexit to destroy this achievement of the Good Friday Agreement," he said.
By BBC Political Correspondent Adam Fleming
There is a lively debate about whether the Irish government has a veto over the decision - to be taken at the summit of EU leaders on 14 and 15 December - about whether Brexit talks can move to the next phase.
Call it what you like, but now Donald Tusk has told us for sure that the rest of the EU will do what Ireland decides.
There was a put-down for British politicians who may find it "hard to understand" why this is important.
But there was some comfort for the British government: Donald Tusk shares their view that the issue of the border can only be solved when there is more clarity about the UK's future relationship with the EU.
And Mr Tusk ended by saying "the key to the UK's future lies - in some ways - in Dublin." Is this a hint that the Irish government's suggestion that Northern Ireland remain in the EU's single market and customs union is the answer for the whole of the UK?
Or is it just a reminder that Dublin is first among equals among the remaining 27 members of the EU?
"The UK started Brexit and now it is their responsibility to propose a credible commitment to do what is necessary to avoid a hard border.
"As you know, I asked Prime Minister May to put a final offer on the table by the 4th of December so that we can assess whether sufficient progress can be made at the upcoming European Council.
"Let me say very clearly. If the UK offer is unacceptable for Ireland, it will also be unacceptable for the EU."
The taoiseach thanked Mr Tusk for the solidarity demonstrated by all EU partners and called the EU "a family which sticks together".
He said he was optimistic that a deal could be achieved by Monday.
However, he said any UK offer must indicate how a hard border can be avoided and avoid the risk of regulatory divergence.
On Thursday, the DUP's Sammy Wilson said any attempt to "placate Dublin and the EU" could mean a withdrawal of DUP support at Westminster.
He was responding to reports of a possible strategy to deal with the Irish border after Brexit.
The story suggested that British and EU officials could be about to seek separate customs measures for Northern Ireland after the UK leaves the European Union.
The DUP struck a deal with Prime Minister Theresa May's government in June, agreeing to support Tory policies at Westminster, in return for an extra £1bn in government spending for Northern Ireland.

A former top trade adviser to US President Trump has told the BBC "there is a level of panic" around Brexit "that is not justified".
Stephen Vaughn, who served as acting trade representative before becoming general counsel on trade, stressed the UK has "enormous leverage" in a potential trade deal with the US.
On a deal's likelihood, he said the Trump administration is "ready to go".
The UK will be able to strike its own trade deals only after leaving the EU.
As a member of President Trump's negotiating team, Mr Vaughn had a key role in the talks with Canada and China, before leaving the administration in April.
In reference to a potential UK deal, he compared the situation with US-Canada negotiations: "No one would say, 'Canada has to join the US in a union or Canada will get steamrolled by the US'."
"You have an enormous amount of leverage, and we'll see how you use it," he added, speaking in his first broadcast interview since leaving the Office of the US Trade Representative.
On US preparations for a potential deal with the UK, he said that Robert Lighthizer, the current US Trade Representative, had done all the preparations needed.
However, he acknowledged that agreeing a deal could take "months or years".
The US Trade Representative, sometimes shortened to USTR, is the president's top adviser on international trade. The team negotiates directly with foreign governments to create trade agreements and participate in global trade policy organisations.
Concerns have been raised over the impact of a deal on life in the UK, including whether US drugmakers would demand the ability to sell to the NHS.
Another key export for the US is agricultural products, but the fact farming methods in the US don't fall under the EU regulations has led some to worry about food standards.
Mr Vaughn emphasised that the US would like a deal to involve the expansion of farm exports, saying he doesn't think it's "something people should be afraid of".
The trade expert, who now works in the private sector, also played an active role in the Trump administration's trade war with China.
He said that a key aspect of those talks was to make sure the two sides comprehended each other: "You really just want to make sure everybody is understanding the issues and what is at stake."
He added that the talks are very "serious" and there is no "yelling and screaming".
Mr Vaughn stressed that the US is concerned about various Chinese practices and that it wants to see Chinese businesses become more "market-oriented".
He went on to defend the use of tariffs against China: "You're trying to figure out, how do you get leverage on the other people?", he explained, adding that Mr Trump is not satisfied with the status quo he inherited.
On the impact of tariffs, he rejected the idea that the measures may be having a negative effect on US business.
"When you look at the actual data, we have by far the largest economy in the G7 and our manufacturing sector continues to grow," he argued.
US business groups have called for a rethink on tariffs, including the National Retail Federation, which has complained about the administration "doubling down on a flawed tariff strategy".
The former top adviser to President Trump, Gary Cohn, has also warned that the tariffs are backfiring.
Speaking in an earlier interview with the BBC, Mr Cohn criticised the approach the Trump administration is taking against China, saying: "I think everyone loses in a trade war."
Mr Cohn, who served as director of the National Economic Council in the Trump administration, announcing he was resigning after Mr Trump decided to impose import tariffs on steel and aluminium.
Mr Vaughn became the acting USTR on Trump's inauguration day in January 2017, staying on until Mr Lighthizer was confirmed in May 2017. He served as Mr Lighthizer's general counsel until the end of April 2019.
Before entering the White House, he was a partner at US law firm King & Spalding, a role to which he has returned.
On his departure, a statement by Mr Lighthizer read: "Stephen has played a central role in shaping and implementing the President's trade policies."

Theresa May has renewed her efforts to sell her draft Brexit withdrawal agreement - arguing it will stop EU migrants "jumping the queue".
She said migration would become skills-based, with Europeans no longer prioritised over "engineers from Sydney or software developers from Delhi".
The PM also insisted to business leaders at the CBI that the withdrawal deal had been "agreed in full".
Nicola Sturgeon said the PM's remarks on EU free movement were "offensive".
The Scottish First Minister said for the prime minister to use such language to describe reciprocal arrangements entered into freely by the UK - allowing EU nationals to live and work in the UK and vice-versa - was "really disgraceful".
Meanwhile, the DUP, which is opposed to the Irish border backstop proposal in the withdrawal agreement, abstained on amendments to the Finance Bill in the Commons on Monday evening.
It also supported one amendment proposed by the Labour Party.
The DUP has a so-called confidence-and-supply arrangement to support the Conservative Party, which does not have a majority in the House of Commons, which was secured with a controversial £1bn funding deal for Northern Ireland.
The party's Brexit spokesman, Sammy Wilson, told BBC's Newsnight the abstentions were made because the government had broken a fundamental agreement to deliver Brexit for the people of the UK "as a whole" and to not "separate Northern Ireland constitutionally or economically from the United Kingdom".
The move was designed to send a political message back, he said.
"'Look, we've got an agreement with you, but you've got to keep your side of the bargain, otherwise we don't feel obliged to keep ours.'"
A senior DUP source stressed, however, that this was not the end of the confidence-and-supply agreement between the Conservatives and the DUP.
Also on Monday evening, the government said it would publish an economic analysis comparing the costs and benefits of its Brexit deal with those of the UK staying in the EU.
A cross-party group of MPs had proposed an amendment to the Bill calling on ministers to publish the forecasts.
The government said MPs would be given the analysis before the meaningful vote on the final deal. It will look at a no-deal scenario, a free trade agreement and the government's proposed deal.
The prime minister's appeal to business leaders came as Tory MPs continue to press for late changes to the deal.
Ministers from the remaining 27 EU countries have met in Brussels to work on the political declaration setting out their future relationship with the UK - a meeting which revealed Spanish concern at the wording's impact on Gibraltar's future.
Meanwhile, Labour leader Jeremy Corbyn, whose party is set to reject Mrs May's deal, told the CBI business lobby group's conference that Brexit can be a "catalyst for economic transformation" in the UK.
There has been widespread criticism of the draft 585-page withdrawal agreement - and the short paper setting out what the UK and EU's future relationship could look like - which are set to be finalised and signed off at an EU summit this weekend.
Two of the prime minister's cabinet ministers resigned over the proposed deal, while others are believed to be trying to change its wording.
Speculation continues over whether the number of Tory MPs submitting letters of no-confidence in Mrs May will reach the 48 required to trigger a confidence vote on her leadership of the Conservative Party.
Mrs May told the CBI's annual conference in London that her plan would provide a fair immigration system that would help young people in the UK get jobs and training.
"It will no longer be the case that EU nationals, regardless of the skills or experience they have to offer, can jump the queue ahead of engineers from Sydney or software developers from Delhi.
"Instead of a system based on where a person is from, we will have one that is built around the talents and skills a person has to offer."
She also said she was not willing to reopen discussions with Brussels over the withdrawal agreement, saying "the core elements of that deal are already in place".
She said that she expected to hammer out a framework for a future trade relationship in Brussels this week, before signing off the deal on Sunday.
CBI president John Allan urged MPs to back Mrs May's deal - despite it not being "perfect" - and warned of the consequences for businesses if the UK were to simply crash out of the EU.
The Labour leader said Mrs May's "botched" deal "breaches the prime minister's own red lines" and "makes no mention of retaining frictionless trade".
Mr Corbyn suggested the EU would consider re-writing the draft agreement "at the 11th hour" if MPs rejected the proposals.
He also suggested the UK's exit from the EU should be a catalyst for far-reaching economic and social change and a "radical programme of investment" in infrastructure, education and skills.
The draft document sets out the terms of the UK's departure, including how much money will be paid to the EU, details of the transition period, and citizens' rights.
The transition period - currently due to last until 31 December 2020 - will mean the UK is officially out of the EU, but still abiding by most of its rules. During this time, the two sides hope to negotiate a permanent trade deal.
The UK and the EU want to avoid a hard Northern Ireland border whatever happens, so they agreed to a "backstop" - described as an insurance policy by Mrs May - aimed at achieving this if the sides cannot agree a trade deal that avoids a physically visible border.
The backstop would mean Northern Ireland would stay more closely aligned to some EU rules, which critics say is unacceptable. And the whole of the UK would be in a single custom territory - effectively keeping the whole of the UK in the EU customs union.
The critics say that during the transition period, the UK will still abide by most of the EU's rules but have no power over setting them - and there is no system for the UK being able to leave any backstop deal without the EU's agreement, so it could become a permanent arrangement.
When asked whether the transition period could last until the end of 2022, Business Secretary Greg Clark told BBC Radio 4's Today programme: "It would be at our request and that would be a maximum period."
He said it could be extended for a matter of "weeks or months", and added: "If we were six weeks away from concluding a future economic partnership and agreeing that, then it may make sense to extend the transition period."
Later, Mrs May told the CBI conference that it was "important" to be out of the implementation period before the next general election - which is due in June 2022.
Environment Secretary Michael Gove, one of the five cabinet ministers who were believed to be trying to change the wording of the deal, said on Monday that the prime minister "has my full support" and she is doing a "very good job".
"I hope people will get behind her as she endeavours to get the very, very best deal for Britain," he said.
But former Foreign Secretary Boris Johnson used his column in Monday's Daily Telegraph to renew his criticism of the draft agreement, describing it as a "585-page fig-leaf [that] does nothing to cover the embarrassment of our total defeat".
And former Tory leader Lord Howard told BBC Radio 4's Today programme that a vote of confidence would be a distraction.
Guy Verhofstadt, the European Parliament's Brexit co-ordinator, said any suggestions EU nationals had been given preferential treatment were wrong since they were merely "exercising rights which provided freedom and opportunities".
Michel Barnier, the EU's chief Brexit negotiator, called on all parties to "remain calm" and focus on the future agreement.
Speaking at a press conference in Brussels after meeting the 27 other EU member states, he said the withdrawal deal was "fair and balanced" but made clear a transition period extension could not be indefinite, "it has to be a fixed period of time".
During Monday's meeting, the Spanish government raised concerns about two articles in the withdrawal agreement (184 and 3), saying that taken together they add up to Gibraltar remaining permanently as UK territory.
The BBC's Brussels reporter Adam Fleming says most member states, along with the European Commission and the European Council, do not agree with Madrid's reading of the text and are seeking to provide reassurance.

Former Conservative Deputy Prime Minister Lord Heseltine has been sacked as a government adviser after rebelling over Brexit in the House of Lords.
Lord Heseltine backed the demand for a parliamentary vote on the final deal to be written into Brexit legislation.
He learned hours later on Tuesday that he had been fired from five government advisory roles he had held.
He said he accepted Number 10's right to sack him but "sometimes there are issues which transcend party politics".
Asked what he thought his sacking said about the current government, he told BBC Radio 4's Today: "I have never met Theresa May so I can't make a judgement. She's doing very well in the polls... the public approve of what she's doing."
Lord Heseltine, who campaigned to remain in the EU, told the Lords that the UK was facing "the most momentous peacetime decision of our time".
The peer said he was having dinner with his wife when he got a call from the chief whip, and went to the Lords to be told he was being sacked.
Lord Heseltine told the BBC the prime minister was "exercising her perfectly legitimate right to get rid of opposition in any way she finds appropriate".
"Whether it's a wise thing to do is a matter for her not for me," he said.
"I have been hugely proud of the work I have done for David Cameron and now for this prime minister, and if they don't want me to go on they must sack me."
He said it was a "great disappointment" for him as "for six years I have had the incredible privilege of working inside the Whitehall machine with civil servants helping ministers to make decisions".
Lord Heseltine continued: "I did write a newspaper article the other day setting out exactly what I intended to do so I think they could have told me this would be the price, but let me make it quite clear; I would still have voted as I did tonight.
"Sometimes in politics there are issues which transcend party politics; in the end you have to be your own person. I believe our interests are intertwined with Europe. I am not prepared to change.
"Every Conservative prime minister I worked for has told me, including this prime minister before the referendum, that we were essentially seeking British self-interest in Europe.
"It's not perfect but it's much better than anything that happened before the Second World War."
The 83-year-old - who dramatically walked out of Mrs Thatcher's cabinet during a row over Westland helicopters in 1986 - served as a minister in both her and John Major's Conservative governments in the 1980s and 1990s.
Who is Lord Heseltine?
Nicknamed "Tarzan" because of his combative manner and long blond hair, renowned by the press as a Conservative "big beast", Michael Heseltine has been a major figure on the UK political scene for decades.
Having made a fortune in publishing, he was an MP from 1966 to 2001.
After Margaret Thatcher came to power in 1979, the ambitious and politically centrist Heseltine became environment secretary and then defence secretary.
But he and his boss had a huge fall-out in 1986, over a complex dispute involving the future of Westland helicopters. He quit and walked out in the middle of a cabinet meeting.
Heseltine remained on the backbenches until, in 1990, with Thatcher apparently losing popularity among the public and her own party, he launched a leadership bid. He didn't win but inflicted enough of a blow on the PM's prestige for her to resign.
John Major won the next contest, but Heseltine, an ardent Europhile, returned to the cabinet, rising to deputy prime minister in the last two years of Major's premiership, a period beset with Conservative disputes over the UK's relationship with the EU.
Heseltine retired as an MP and entered the Lords, where he continued occasionally to speak out on issues dear to his heart - including putting the Remain case during the EU referendum campaign - and also returned to publishing.
Lord Heseltine was brought in by former Prime Minister David Cameron to advise the government on a range of projects, including schemes in east London and Swansea.
He told Today that his roles were taking up three to four days a week.
A Downing Street spokesman said he understood Mrs May had in fact met Lord Heseltine, although he did not confirm whether this was before or after she became prime minister.
In a statement, the government said it had "a clearly stated and consistent position" that the Brexit bill should be passed without amendment.
The chief whip in the Lords asked Lord Heseltine to stand down because he voted against the government's official position, it said, adding: "The government would like to warmly thank Lord Heseltine for his service."
Former Tory chief whip Mark Harper said it was "quite reasonable" to sack Lord Heseltine for opposing government policy.
Brexit Secretary David Davis has said some in the Lords are seeking to "frustrate" Brexit but it was the government's intention to ensure that did not happen.
When the bill returns to the Commons next week ministers will have some persuading to do to reverse the Lords changes, but Theresa May remains on course to trigger Article 50 and begin Brexit negotiations before the end of this month.
Peers voted by 366 votes to 268 in favour of an amendment to the bill to have a "meaningful" parliamentary vote on the final terms of the Brexit deal.
It was the second defeat for the bill in the Lords - the previous one was on the issue of guaranteeing the rights of EU citizens.
After a three-hour debate on Tuesday, the turnout for the vote was the largest in the Lords since 1831, according to Parliament's website.
As well as Lord Heseltine, 12 other Tory peers defied the government to vote in favour of the amendment, including former ministers Lord Deben and Viscount Hailsham.
Mrs May has said she wants to trigger Article 50 by the end of March but the Commons is unlikely to have an opportunity to consider the changes made by the Lords until the middle of next week because four days have been set aside for debate on the Budget.

The government has seen off an attempt to add conditions to its Brexit bill as a Conservative rebellion was avoided.
MPs rejected a bid by Labour's Chris Leslie to force the government to consult Parliament on the deal struck with the EU before it is finalised.
It came after ministers pledged that a "meaningful" vote would be offered.
Labour and some Tories had pushed for MPs to have a decisive say on the final terms, but the 326 to 293 vote meant the bill remained unchanged.
Seven Conservatives rebelled, while six Labour MPs voted with the government.
Several other attempts to amend the draft legislation, which if passed will authorise the prime minister to formally begin Brexit negotiations under Article 50 of the Lisbon Treaty, were also rejected during more than seven hours of debate.
More amendments will be considered on Wednesday before MPs hold a final vote on whether to back the bill.
Theresa May has already promised Parliament will get a say on the final deal, but critics, including some Conservatives, said they wanted more than the "take it or leave it" vote being offered.
Any possibility of a major Conservative rebellion appeared to be halted by comments from Brexit Minister David Jones.
Mr Jones said MPs would get a say on the final draft Brexit agreement before it was voted upon by the European Parliament.
"This will be a meaningful vote," he told MPs.
"It will be the choice of leaving the EU with a negotiated deal or not."
However, some MPs questioned whether any concessions had in fact been offered, with Downing Street playing down claims the government's position had changed.
Asked what would happen if Parliament rejected the Brexit deal or if there was no agreement with the EU to vote upon, Mr Jones said that in each scenario the UK would still leave the EU but "fall back on other arrangements".
This would effectively see the UK default to World Trade Organization trade rules, involving potential tariffs on exports and imports.
Opponents of Brexit have said this would cause real damage to British business, but supporters say the UK can live with the consequences if necessary as the UK would then be free to negotiate its own trade arrangements.
Mr Jones said the government wanted to avoid a situation in which ministers were  sent back to the negotiating table to hammer out a better deal.
This, he said, would be hard given the two-year limit for talks and would also be "the surest way of undermining our negotiating position and delivering a worse deal".
Former chancellor Ken Clarke - the only Tory to vote against kickstarting the Brexit process last week - said Parliament should have the opportunity to shape the final deal, while former SNP leader Alex Salmond said MPs should have a genuine choice without the "Sword of Damocles" hanging over them.
Labour's Chuka Umunna said the choice facing MPs was "unacceptable", ex-Lib Dem leader Nick Clegg described it as a "symbolic handout" while Green Party leader Caroline Lucas said MPs were being "duped".
But Labour's font bench claimed the move as a "significant victory" in response to its repeated demands for a "meaningful" vote at the end of the two-year negotiation process.
The party withdrew its proposed amendment before Mr Leslie's was defeated.
Conservatives Mr Clarke, Bob Neill, Andrew Tyrie, Claire Perry, Anna Soubry, Antoinette Sandbach and Heidi Allen, defied their party whip.
Ms Perry told MPs the tone of the debate "sometimes borders on the hysterical", before adding: "I feel like sometimes I am sitting along with colleagues who are like jihadis in their support for a hard Brexit."
Teasing her colleagues, she said: "No Brexit is hard enough - 'begone you evil Europeans, we never want you to darken our doors again'. People say: 'Steady on, Claire', but I am afraid I heard speeches last week exactly making that point."
On the Labour benches, Frank Field, Ronnie Campbell, Kate Hoey, Kelvin Hopkins, Graham Stringer and Gisela Stuart voted with the government.
Labour leader Jeremy Corbyn, who backed the Remain side in last year's EU referendum, has ordered his MPs to support the government's bill, whether his party's amendments are accepted or not, in the third reading vote expected on Wednesday.
Mr Corbyn argues that it would be undemocratic to ignore the will of the people, as expressed in last June's EU referendum.
Shadow business secretary Clive Lewis has vowed to oppose the bill unless Labour amendments are passed in the Commons.
Frontbench members of parties are generally expected to resign from their post if they ignore a three-line whip.

Another Brexit referendum will become a "plausible" way forward if there is deadlock in Parliament, Work and Pensions Secretary Amber Rudd has said.
She told ITV's Peston show while she did not personally support another vote, the case for one would grow if MPs could not agree another solution.
She said she hoped MPs would back Theresa May's deal with the EU next month but it would be "very difficult".
The PM says the UK must be ready to leave without a deal if it is rejected.
Mrs May has repeatedly ruled out holding another referendum, saying it was the government's duty to implement the result of the 2016 Brexit vote.
A Downing Street source said the government was "very clear we are 100% opposed" to another referendum.
The UK is due to leave the EU on 29 March 2019 but an agreement on the terms of its withdrawal and a declaration on future relations will only come into force if the UK and EU Parliaments approve it.
The Commons vote was due to be held earlier this month but the PM postponed it once it became clear it would be defeated by a large margin.
She has since sought to gain further assurances from EU leaders to allay MPs' concerns.
Ms Rudd told Robert Peston she could not be sure MPs would back the deal. She suggested arguments for another referendum would come into play if they did not and if they rejected other options.
"I have said I don't want a People's Vote or referendum in general but if parliament absolutely failed to reach a consensus I could see there would be a plausible argument for it," she said.
"Parliament has to reach a majority on how it is going to leave the EU. If it fails to do so, I can see the argument for taking it back to the people again as much as it would distress many of my colleagues."
If Mrs May's deal is rejected, the default position is for the UK to leave in March unless the government seeks to extend the Article 50 negotiating process or Parliament intervenes to stop it happening.
Ms Rudd, who has likened the idea of a no-deal exit to a car crash, said it was imperative that MPs "find a way of getting a deal through Parliament".
To that end, she said she backed the idea of testing the will of Parliament through a series of "indicative" votes on "Plan B" options should MPs reject the PM's agreement.
"It would flush out where... the majority is," she said. "So people who hold onto the idea of one option or another would see there is no majority and so they will need to move to their next preference.
"We will hopefully be able to find where the compromise and the consensus is."
Speaking on the same programme, Labour's shadow education secretary Angela Rayner said talk of another referendum was "hypothetical" at this stage and would represent a "failure" by Parliament.
She accused the prime minister of trying to scare MPs into backing her deal by delaying the vote on it to the latest possible date.
Earlier on Wednesday, the European Commission announced a series of temporary measures designed to reduce the economic impact if the UK was to leave without a comprehensive legally-binding agreement.
But it made clear that it could not counter all the problems it expects.
The Republic of Ireland has given more details of its own no-deal contingency planning, saying the risk of the UK leaving without an agreement was "very real".
It warns of potentially "severe macroeconomic, trade and sectoral impacts" for Ireland as well as "significant gaps" in policing and judicial co-operation.
In such a scenario, it said its priorities would be to uphold the Common Travel Area between the UK and Ireland, ensure there is no return of physical checks on the border between the Republic and Northern Ireland and ensure the "best possible outcome" in terms of trade.
The UK has allocated a further £2bn in funding to government departments to prepare for the possibility and has urged businesses to put their own no-deal plans in motion.

The woman who brought the successful legal challenge against the government over Brexit has accused prominent politicians of behaving "despicably".
Gina Miller told the BBC they had "exacerbated" worries during and after the EU vote and failed to defend her and others with "legitimate concerns" about the process in the face of abuse.
She insists she did not bring her case to thwart the UK's exit from the EU.
But she said some politicians were in "la la land" about what lay in store.
The investment manager was speaking to the BBC's political editor Laura Kuenssberg after the Supreme Court upheld her challenge to the government's approach.
By a margin of eight to three, the justices ruled that Parliament must give its consent before Theresa May can start official talks on the terms of the UK's exit.
Ministers say it was right for the court to decide and they will comply with the ruling.
Mrs Miller, who voted to remain in the EU, said she felt vindicated but that her goal all along had been to give a voice to the millions of people with a stake in the process and help deliver "the best Brexit we can get".
"This is about right and wrong, it's wrong that a government think they are above the law. It's right that I can bring this case," she said.
The 51-year old, who was born in Guyana but educated in Britain, suggested the EU referendum had created a climate of fear in which anyone asking questions about Brexit was seen as unpatriotic and "branded as traitors".
"There's this sense that if you ask a question about Brexit then you're not representing Britain," she said. "Asking questions about Brexit is the most patriotic thing you can do."
She added: "People voted because of legitimate concerns. Politicians have behaved despicably because they have exacerbated those anxieties."
Asked if Theresa May and her ministers had behaved "despicably", Ms Miller said it was "wrong of them not to stand up earlier when the judges were being vilified".
"I think it was wrong of them to not actually speak up sooner about abuse for not just myself but for other people who live in the UK."
Mrs Miller, who says she has been subjected to constant abuse including death threats, said she felt her "family and safety have been put in jeopardy".
"The idea that as a woman I had no right to speak out and I'm not bright enough to speak out. And as an ethnic woman I have no place in society. That's worrying."
She said she was still concerned that politicians were "twisting the truth" when it came to the UK's future outside the EU and Mrs May and her ministers needed to "be honest" with the public about what was achievable from the negotiations.
"Even now, some of the things I hear about what is possible, as we progress Brexit, it's as though they are living in some sort of la la land because it's pure fantasy."
She added: "There are 27 other member states on the other side of the table who are not just going to give us what we want. They are not going to give us cherry picking".

The Lord Chancellor has backed the independence of the UK's judiciary but stopped short of condemning attacks on senior judges over the Brexit ruling.
The Bar Council had demanded Liz Truss respond to criticism from some MPs and newspapers over the decision that MPs should vote on triggering Article 50.
The Daily Mail branded judges "Enemies of the people"; the Daily Express said it was "the day democracy died".
Ms Truss said the "impartiality" of the courts was "respected the world over".
On Thursday, the High Court ruled Parliament should vote on when the government can trigger Article 50, beginning the formal process of the UK leaving the EU.
Three judges found that the government could not start the formal process by using the royal prerogative alone, and would need the backing of both the Commons and the Lords.
The government is seeking to overturn the decision at the Supreme Court - the UK's highest court of appeal - next month.
Following fierce criticism of the ruling, the Bar Council of England and Wales - the professional body representing barristers called for Ms Truss to defend the judges "as a matter of urgency".
But its chairwoman Chantal-Aimee Doerries QC said she would have expected the Lord Chancellor - who is responsible for courts, prisons, probation and constitutional affairs - to make a clearer statement on the "unprecedented" attack which  "undermines the rule of law in this country".
She said the court was entitled to rule on the case and she was "surprised by the backlash" because the judges were "doing their job".
The Criminal Bar Association later passed a resolution backing the Bar Council's demands.
In her statement, Ms Truss, who is also justice secretary, said: "The independence of the judiciary is the foundation upon which our rule of law is built and our judiciary is rightly respected the world over for its independence and impartiality.
"In relation to the case heard in the High Court, the government has made it clear it will appeal to the Supreme Court. Legal process must be followed."
By Ben Wright, BBC News political correspondent
It could not be called a comprehensive response.
Having declined all requests for an interview, the Lord Chancellor Liz Truss put out a three-line statement saying the judiciary was independent and impartial.
Considering the vitriol of some press reaction to the High Court judges decision - "enemies of the people" according to the Daily Mail - and the demands for a defence of the judiciary from Labour and prominent Tory MPs, the government's response was the bare minimum.
We know ministers are angry about the ruling and are appealing to the Supreme Court.
But given a chance to say newspapers and politicians should be very wary about attacking the judiciary the Lord Chancellor demurred.
Nor did she say the courts did have the jurisdiction to rule on this dispute.
However, it be a very brave (or foolish?) minister to criticise the press for writing what they like about Brexit. And many voters will share the anger of some newspapers about the decision of the court.
Shadow justice secretary Richard Burgon, who had earlier said Ms Truss's silence was "embarrassing", called her statement "too little, much too late" and said she had failed to "adequately stand up to attacks on [the] judiciary".
He said "pressure from the legal profession, professional bodies, politicians and the public has paid off" and Ms Truss had "finally made at least some progress on this issue".
But he added: "All Liz Truss has done is recite the well-known principle of the independence of the judiciary...
"The last few days mean that much of the legal community now has no confidence in the Lord Chancellor to fulfil her statutory duty to protect the independence of the British judiciary."
Writing on Twitter, Lib Dem leader Tim Farron described the response from Ms Truss as a "weak statement from a weak cabinet minister".
Earlier, Tory MP and former Attorney-General, Dominic Grieve, has compared coverage in one UK newspaper to the Nazi party's newspaper.
He told BBC Radio 5 live: "Newspapers in a free society can do what they like.
"But if you did decide to behave immoderately and whip up frenzied hatred you can do that in a free society if you set about it, and newspapers like the Daily Mail are no different from the Voelkischer Beobachter in Nazi Germany if they run headlines of that type."
Daily Mail columnist Stephen Glover defended his newspaper's stance, saying he did not believe the judges would "feel frightened or worried" by the criticism.
He said they had made a "decisive intervention" in the political process, and "must expect some comeback".
UKIP MP Douglas Carswell is among those who have attacked the judges, calling them "politicians without accountability".
Meanwhile, Gina Miller, the investment manager and philanthropist who led the legal campaign, has said she plans to report online trolls to police after receiving rape and death threats.
"I am really cross at the politicians and the media who are whipping this up because they are the ones inciting racism and violence and acrimony," she said.
The Archbishop of Canterbury, Justin Welby, also commented on the row, writing in a tweet: "Horrified by trolling of judges & those going to court; British values call for honest but good disagreeing, need reconciliation not abuse".
He added independent judges were "fundamental to our values" and it was "wrong to attack them for declaring the law",
Prime Minister Theresa May has said she is "confident" the government will win its Supreme Court appeal and is committed to triggering Article 50 by March 2017.

The European Court of Justice has ruled the UK can cancel Brexit without the permission of the other 27 EU members.
The ECJ judges ruled this could be done without altering the terms of Britain's membership.
A group of anti-Brexit politicians argued the UK should be able to unilaterally halt Brexit, but they were opposed by the government and EU.
The decision came as Theresa May announced a Commons vote on whether to approve her deal would be postponed.
MPs had been widely expected on Tuesday to reject the EU withdrawal agreement negotiated by Mrs May.
But she pre-empted their decision, saying the vote would be deferred to a later date so she could seek "further assurances" from EU leaders about the application of the Irish border backstop.
In a subsequent statement to MPs, Brexit Secretary Steve Barclay said the government noted the ECJ ruling but insisted "our policy has not changed".
He said the UK would be leaving the EU on 29 March 2019, under the terms of the EU's Article 50 process, and had "absolutely no intention" of overturning the 2016 Brexit vote.
"The government's firm and long held policy is that we will not revoke the Article 50 notice," he said.
The case was brought by a cross-party group of Scottish politicians and the Good Law Project who wanted to know whether the UK could revoke the decision to leave the EU without getting approval from the other member states.
They believed that if the ruling went in their favour, it could pave the way for an alternative option to Brexit, such as another referendum.
Both the UK government and the EU had been against it going to the ECJ.
The EU warned that it would set a dangerous precedent by encouraging other countries to announce they were leaving in an attempt to secure better membership terms, before cancelling their withdrawal.
The UK government's lawyers also argued that the case was purely hypothetical as "the UK does not intend to revoke its notification" and those politicians behind it wanted to use the case as "political ammunition to be used in, and to pressure, the UK Parliament".
The ECJ ruled that the UK can unilaterally revoke its withdrawal from the EU, broadly following the non-binding opinion given last week by a senior ECJ official - the advocate general.
The statement from the court said the ability for a member state to change its mind after telling the EU it wanted to leave would last as long as a withdrawal agreement had not been entered into, or for the two-year period after it had notified the bloc it was leaving.
If that two-year period gets extended, then a member state could change its mind during that extra time too.
The court said the UK would be able to stay on the same terms it has now, so it would not be forced to join the euro or the Schengen area - where there are no passport controls between countries.
But the decision to stay must "follow a democratic process".
The member state would then have to write to the EU to notify them of the "unequivocal and unconditional" decision.
The ECJ said it made the ruling to "clarify the options open to MPs" ahead of voting on Mrs May's deal.
The politicians involved hope the victory will increase the chances of Brexit being called off completely, potentially through another referendum.
Scottish Green MSP Ross Greer - one of the politicians who launched the case - said: "This is a massive moment at the start of a vital week, pointing to a clear way out of the Brexit mess."
And the SNP's Alyn Smith, who was also involved in the case, said: "A bright light has switched on above an exit sign."
Jolyon Maugham QC, director of the Good Law Project which took the case to the court, said that the ruling was "arguably the most important case in modern domestic legal history".
"It is up to MPs to remember what they came into politics for and find the moral courage to put the country's interests before private ambition," he added.
Scotland's First Minister Nicola Sturgeon - who backed Remain - said the ruling meant it was "now open to the House of Commons" to extend Article 50 to allow time for another vote.
And Lib Dem Brexit spokesman Tom Brake tweeted that it was the "best news possible" and said it was now "full steam ahead for a People's Vote".
Environment Secretary Michael Gove, a prominent Brexiteer, told BBC Radio 4's Today programme those calling for a second vote were "people who never accepted that first vote, who didn't accept that democratic mandate and who want to overturn it".
"We don't want to stay in the EU. We voted very clearly, 17.4 million people sent a clear message that we want to leave the European Union, and that means also leaving the jurisdiction of the European Court of Justice," he added.
"So, this case is all very well, but it doesn't alter the referendum vote or the clear intention of the government to make sure that we leave on 29 March."
Foreign Secretary Jeremy Hunt told the BBC people would be "shocked and very angry" if any government delayed leaving the EU and it was "certainly not the intention of the government".
Brexiteer Tory Jacob Rees-Mogg hailed the decision as the right one, but told LBC radio: "I think this government would find it very difficult to remain the government if it went away from what it said in its manifesto and the referendum result."
A spokeswoman for the European Commission said it would "take note" of the judgement, but there was an "agreement on the table".
"As President [Jean-Claude] Juncker said, this deal is the best and only deal possible. We will not renegotiate," he said.
"Our position has therefore not changed and as far as we are concerned the United Kingdom is leaving the European Union on the 29 March 2019."
BBC Brussels correspondent Adam Fleming said the ruling made staying in the EU "a real, viable option" and that may "sway a few MPs" in the way they vote.
But he said "a lot would have to change in British politics" to see the UK remain in the EU, with Mrs May and the government having to change its mind to make it a "political reality".

Dundee will not be able to compete in the European Capital of Culture 2023 competition due to Brexit, the European Commission has confirmed.
Five UK cities were bidding to host the title, with the winner expected to be announced next week.
A letter from the European Commission to the Department of Digital, Culture, Media and Sport (DCMS) said UK participation "would not be possible".
It said the UK's selection process should "immediately be discontinued".
Dundee's bid team were due to make their final presentation to the competition judges next week.
BBC Scotland understands that the DCMS only received the Commission's letter on Wednesday.
A Dundee 2023 spokesman said that the team was "hugely disappointed" at the European Commission's late decision.
He said: "The timing is disrespectful not only to the citizens of Dundee, but to people from all five bidding cities who have devoted so much time, effort and energy so far in this competition.
"It's a sad irony that one of the key drivers of our bid was a desire to further enhance our cultural links with Europe."
The UK's five final bid proposals were submitted at the end of October.
They were Dundee, Nottingham, Leeds, Milton Keynes, and a joint proposal from Belfast, Londonderry and Strabane.
Dundee's 80-page bid document was understood to include 110 new projects across the city.
Scotland's culture secretary Fiona Hyslop said: "It is now deeply concerning that the amount of time, effort and expense Dundee have put into scoping out their bid could be wasted thanks to the Brexit policy of the UK government .
"We are in urgent contact with the UK government and Dundee to understand the potential implications of this situation and to establish what action the UK Government is going to take to address it."
The DCMS said it "disagreed" with the European Commission's stance and was "deeply disappointed" that the Commission had waited until the UK cities had submitted their bids before "communicating this new position to us".
The UK government said previously that the title was "part of our plan for a dynamic, outward-looking and global Britain" post-Brexit.
However, it had warned bidders that the contest "may be subject to the outcome of those exit negotiations".
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Welsh politicians have clashed over Theresa May's announcement that the UK should leave the EU single market.
In a speech, the prime minister said staying in the single market would mean "not leaving the EU at all".
First Minister Carwyn Jones said he would still push for "full and unfettered access" to the single market, while Plaid Cymru MP Jonathan Edwards warned of an "extreme Brexit".
But Welsh Tory leader Andrew RT Davies denied it would damage the economy.
In a long-awaited speech, Mrs May said Parliament would get a vote on the final deal agreed between the UK and the European Union.
She promised an end to "vast contributions" to the EU, and said the devolved administrations would be "fully engaged" in the process of negotiating Brexit.
"I should equally be clear that no decisions currently taken by the devolved administrations will be removed from them," Mrs May.
First Minister Carwyn Jones told AMs that the prime minister spoke to him on the phone before her speech.
"Some of it was welcome ... the tone was better", he said during First Minister's Questions.
But as well as giving the Houses of Parliament a vote on the final Brexit deal, Mr Jones said the Senedd would need one too, as many of the terms would cover policy areas devolved to Wales.
He added: "There will be nothing to stop this Assembly from implementing European directives if it wishes to.  There is no ban on doing that."
Mr Jones said he would continue to make the case to have "full and unfettered access" to the EU single market, despite Mrs May's insistence that the UK would leave.
"What we have to avoid in the next few months and years is anything that impairs the ability of businesses to export from Wales, and therefore makes it more difficult for them to employ people," he said.
Labour's Shadow Welsh Secretary Jo Stevens added:  "With the PM set on a damaging hard Brexit, I'm fearful Wales will be left behind and made to suffer the terrible consequences of this incompetent Tory government."
Welsh Secretary Alun Cairns said Brexit gave the UK the opportunity to become "global leaders in free trade".
"There are new opportunities out there, the UK economy is exceptionally strong and both Wales and Welsh businesses are set to benefit from that", he said.
Mr Cairns added that he supported leaving the single market, saying the British people "won't accept and can't accept" the free movement of people.
Andrew RT Davies, who leads the Conservatives in the assembly, denied what he called a "clean Brexit" would be damaging to the Welsh economy.
"This was a hugely welcome speech from the prime minister, providing clarity and certainty ahead of the triggering of Article 50," he said.
"The onus now, in many ways, moves on to the EU itself and leaders on the continent will need to determine for themselves if they want to be part of a new trading agreement with the fifth largest economy in the world."
Mr Edwards, Plaid Cymru spokesman on leaving the EU, said:  "The Prime Minister has put the British State on track for an 'extreme Brexit', isolating Wales and the other UK countries from the rest of the world.
"The Prime Minister has put appeasing her deluded right-wing politicians before protecting the economy and surely the Labour Party must now join Plaid Cymru in voting against triggering Article 50.
"The people voted to leave the EU, not the single market or the customs union.
"Nobody voted to make themselves redundant or give themselves a pay cut. For Wales - a country whose economy is heavily dependent on its exports - isolating ourselves from the single market will be disastrous."
He added that "The serious and disproportionate impact this will have on Wales' economy and devolved functions means that Wales' Parliament must also be asked to endorse the terms of the agreement before it goes ahead, not just Westminster."
UKIP's MEP for Wales Nathan Gill welcomed the speech, saying: "Remaining a member of the single market was never an option as it amounted to no Brexit at all.
"Too many of the 'elite' in media and politics are trying to re-live the referendum, rather than respecting the will of the people and moving forward.
"It's clear to me that the best deal for both Wales and the UK would be a free trade deal between the UK and EU, allowing British companies the freedom to trade with and operate in the single market, and let European businesses do the same here.
"It would also bring back control over immigration and end the supremacy of European courts."
While the prime minister said no decisions currently taken by the Welsh Assembly would be removed after Brexit, the Welsh Government is keen to take control of two major issues currently decided at EU level - farming subsidies and economic aid to Wales' poorest areas.
Asked by UKIP AM Mark Reckless about the repatriation of powers from Brussels, the first minister said:  "If you look at agriculture, we take the decisions on agriculture. If you look at fisheries, we take the decisions on fisheries.
"There is no question of there being some kind of UK-wide agriculture policy that's not devolved on the basis of what the Prime Minister said today.  That's quite clear to me."
He said the people of Wales would not want to see "Brussels bureaucrats replaced with Whitehall bureaucrats."

The government has said it will release information from Brexit impact studies, after Labour won a vote effectively forcing their hand.
Ministers had argued that releasing the economic impact studies would undermine their Brexit negotiating position.
But Commons Leader Andrea Leadsom agreed that Wednesday's vote was "binding" and told MPs: "The information will be forthcoming."
Brexit Secretary David Davis said ministers would be "as open as we can".
He said he was already talking to Hilary Benn, the Labour chairman of the Committee for Exiting the European Union, about "how we handle the confidentiality of the documentation we'll hand over".
The government has been under pressure to release the studies, which show the potential impact of leaving the EU on 58 economic sectors.
On Monday it published the list of sectors that have been looked at, ranging from aerospace and aviation to tourism and legal services. But it had argued that releasing them would undermine its negotiating position.
But on Wednesday Labour used an arcane parliamentary procedure to get the documents released.
It involved tabling a motion that "an humble address be presented to Her Majesty" requiring that the reports "be laid before this House and that the impact assessments arising from those analyses be provided to the Committee on Exiting the European Union".
The government chose not to oppose the motion and it was not initially clear whether it would be binding.
Speaker John Bercow told MPs on Wednesday that this type of motion had "traditionally been regarded as binding or effective" and made clear that the government should respond quickly to the vote.
Brexit Secretary Mr Davis told MPs that discussions were under way with Mr Benn about releasing the the documents but added: "These documents are not some sort of grand plan, they're data about the regulations and the markets of individual sectors which inform our negotiation.
"Of course we will be as open as we can be with the select committee, I fully intend to."
In a letter to Mr Davis, Mr Benn asked him to confirm in writing what arrangements he was making to provide his committee with the impact assessments.
He added that he hoped it would be done "much sooner" than the 12 weeks the government had previously indicated it would take to respond to opposition day debate motions.
Earlier Commons Leader Ms Leadsom was asked when the studies would be released. She replied: "It is absolutely accepted that the motion passed by the House yesterday is binding and that the information will be forthcoming.
"But, as I think as has been made very clear, it is the case that it is difficult to balance the conflicting obligation to protect the public interest through not disclosing information that could harm the national interest and the public interest whilst at the same time ensuring that the resolution of the House passed yesterday is adhered to."

Theresa May and EU Commission President Jean-Claude Juncker have agreed to "accelerate" Brexit negotiations - but there was no sign of a breakthrough after their working dinner.
A joint statement said the Brussels talks - which came before EU member states meet to assess progress - were "constructive and friendly".
The UK's financial settlement with the EU continues to be a sticking point.
The EU will not discuss trade until this has been settled.
Mrs May has also spoken to the French and German leaders ahead of the European Council summit.
The EU's chief negotiator Michel Barnier and his UK opposite number, Brexit Secretary David Davis, also joined the working dinner.
"The prime minister and the president of the European Commission reviewed the progress made in the Article 50 negotiations so far and agreed that these efforts should accelerate over the months to come," the statement read.
"The working dinner took place in a constructive and friendly atmosphere."
By Laura Kuenssberg, BBC political editor
Accelerate, accelerate, accelerate, accelerate.
OK, in theory, if I am driving a car at four miles per hour and I speed up to eight miles per hour, technically I am accelerating.
I may still be basically crawling along. I still may be late - very, very late - for my eventual destination. But, by the very action of pressing the pedal and going faster, I am actually speeding up.
If anyone accuses me of going nowhere, or slowing down - well, look at my speedometer. I am going faster and I have evidence that you are wrong!
That is why, in the next few days, don't be surprised if every Tory politician you see, hear, or read about is using that word (at least those loyal to the government) to claim that there is progress in the Brexit talks, just days after the chief negotiator on the EU side declared a deadlock.
BBC Europe correspondent Kevin Connolly said the joint statement released after the dinner was "a masterpiece of uncommunicative communication".
He said: "It recorded formally that Brexit negotiations are taking place between the EU 27 and the UK - a statement of the obvious that may hint at Brussels' displeasure with British attempts to talk directly to individual member states as well."
He added: "The gnomic communique was perhaps an attempt to avoid a repeat of the fallout from the last bilateral dinner in Downing Street in April after which the EU side was reported to have described the British as 'delusional' and even disparaged the food."
Along with the UK's "divorce bill", the EU is insisting agreement be reached on citizens' rights and what happens on the Northern Irish border before agreeing to open talks on the free trade deal Mrs May's government wants to strike.
Last week an internal draft document suggested the EU was going to begin preparing for the possibility of trade talks beginning in December - provided the UK does more to bridge the gap on these key negotiating points.
Speaking on BBC Radio 4's Today programme, Michael Fuchs, the vice chairman of Angela Merkels's Christian Democratic Union party, agreed it was "absolutely necessary" to accelerate the talks, given the two-year timeframe for departure set out by the EU treaties.
But he suggested Foreign Secretary Boris Johnson was thwarting Mrs May's attempts to reach a deal on the financial issue.
"I know there are internal problems, whatever she is offering, Boris Johnson is saying it's too much," he said.
"I don't know what his influence (is), it seems to be pretty strong because otherwise she would come up with other proposals I guess and the problem is she has internal trouble in the Tories."
Speaking in the House of Commons, Mr Johnson said he thought a reported bill of £100bn was too high, accusing Labour of being willing to "cough up" such a sum.
He said the government was united on its Brexit strategy and urged the EU to "get serious" and agree to settle the citizens' rights question.
Meanwhile, a new report suggests that leaving the EU without a trade deal would lead to a significant rise in living costs for millions of people.
Research by the Resolution Foundation and trade experts at Sussex University calculates that the average household would pay an extra £260 a year for imported goods.
For three million households - those who consume the most imported goods - that figure would nearly double to £500 a year.
The report says that without a Brexit deal, European goods would incur the same tariffs as those imposed on other World Trade Organisation countries, increasing levies on dairy products by 45% and meat products by 37%.
But a government spokesperson said ministers were optimistic about achieving an agreement with the EU that would allow for frictionless trade in goods and services.
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Brexit Secretary David Davis has called on both sides in the negotiations on the UK's departure from the European Union to "get down to business".
Mr Davis was in Brussels to launch the second round of formal talks.
He said his priority was to "lift the uncertainty" for EU citizens living in the UK and Britons living in the EU.
The EU says there must be substantial progress on this - and on a financial settlement and the issue of the Irish border - before trade talks can begin.
Appearing alongside EU chief negotiator Michel Barnier, Mr Davis said there had been a good start to the process and it was time to get to the "substance of the matter".
Mr Barnier said the negotiators would "now delve into the heart of the matter".
Talks will cover citizens' rights, finance, Northern Ireland and Euratom, with separate negotiating teams set up for each issue.
A UK government source told the BBC that 98 British officials were in Brussels for the negotiations.
Mr Davis spent two to three hours in the EU quarter, meeting Mr Barnier for between 45 minutes and a hour before returning to London.
The two men are expected to give an update on progress made at a press conference on Thursday.
Earlier this month, Theresa May's offer to give the three million EU citizens in the UK "settled status" after Brexit was immediately dismissed by European Council President Donald Tusk as "below our expectations".
And Mr Barnier has said there were still major differences between the EU and UK on the subject.
Speaking at a separate European Council meeting in Brussels, Foreign Secretary Boris Johnson insisted the UK had made a "very fair, serious offer".
By Kevin Connolly, BBC Europe correspondent
The call to "get down to business" from David Davis is meant to signal that the Brexit talks are entering a serious phase after an opening session of pleasantries and procedural discussions.
That might raise eyebrows on the European side where there's a perception that Britain dithered for months after the Brexit referendum before getting down to talks.
The UK says it's prioritising the issue of mutual citizens rights after its opening proposals received a lukewarm response in Brussels.
The atmosphere around this second round of talks may have been improved a little by a government acknowledgement that the UK has obligations to the EU which will survive withdrawal and which need to be resolved.
Mr Johnson has said that Brussels can "go whistle" if it expected the UK to pay an "extortionate" bill as part of the separation.
The government's official position, confirmed in a Parliamentary statement last week, is that it will "work with the EU to determine a fair settlement of the UK's rights and obligations as a departing member state, in accordance with the law and in the spirit of our continuing partnership".
The EU has insisted that citizen rights - along with the "divorce payment" and border issues - must be dealt with before future UK-EU trade can be discussed.
Sir Keir Starmer, Labour's shadow Brexit secretary, criticised Mr Davis for spending "only a few minutes in Brussels before heading back to Whitehall".
"There is no agreed cabinet position on vital Brexit issues, the negotiating team is not prepared and the Prime Minister has lost her authority," he said, calling for engagement "with the substance of talks".
The Liberal Democrats' Brexit spokesperson, Tom Brake, said Mr Davis' brief visit to Brussels - and a lack of briefing papers on the UK side of the table in when the negotiators posed for a photograph - was proof that government preparation for the negotiations was lacking.
"He didn't have any position papers with him because this government has no agreed Brexit position," he said.
Lord O'Donnell, the UK's former top civil servant, suggested the chances of a smooth Brexit were at risk.

Sandwiches would be one of the first victims of a breakdown in the food supply chain in the event of a disorderly no-deal Brexit, according to a senior grocery executive.
"If you look at the ingredients - a bit of lettuce, tomato, maybe avocado, chicken with a bit of mayonnaise - all prepared fresh and kept chilled, sandwiches would be some of the most vulnerable products if food supply chains were interrupted."
The space between two pieces of bread is perhaps unlikely new territory for Brexit contingency planning but it reflects an area of serious concern that government ministers have been quizzed over this week.
Although they have said they hope and expect a deal to be done - they are making emergency preparations for the potential interruption to vital supplies like fresh food now that they have said planning for "no deal" is being stepped up.
Responses from Brexit Secretary Dominic Raab have been slightly evasive on this issue. When asked by MPs whether the government was stockpiling food he said: "It would be wrong to describe it as the government doing stockpiling but we will look at this issue in the round and make sure that there is adequate food supply."
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Publishers warn Brexit could hit exports
BMW joins Airbus in Brexit warning
This has led to images being conjured of massive warehouses being filled with emergency rations to see the nation through as if on a war footing. So, if the government isn't stockpiling food, is anyone else? Is it even necessary?
Food retailers are understandably reluctant to talk openly about empty shelves but this is what I've learned.
First - every major food retailer I've spoken to is quite clear they have NOT been approached by government to start redirecting any food to some sort of emergency reserve.
"It wouldn't work anyway," said one. "Fifty percent of the food we eat is either fresh or chilled - that includes ready meals - so warehousing wouldn't help".
There is another problem according to another.
"There simply isn't any spare slack in the supply chain to do this. There are no slightly-under-packed lorries or empty warehouses available to do this at scale. To suggest it could even be done if required is incredibly naive."
Most agree there is a real potential threat.
The Beast from the East was essentially two days of snow and it resulted in empty shelves starting to appear in some supermarkets. "Crashing out of the EU without a deal could potentially see the ports overwhelmed, with gridlock that could take days to work through and that would be a massive problem."
So neither the government, nor industry, is stockpiling food - but that does not mean that food retailers aren't making contingency plans.
Most of them get a lot of fresh food from the southern hemisphere in winter and the northern hemisphere from spring onwards - some are looking at extending their southern hemisphere sourcing longer into the spring.
That makes sense according to Lord (Mark) Price, former boss of Waitrose and trade minister. "In late March/early April you would be switching from southern to northern hemisphere providers for some produce so it would make sense to stretch that."
Lord Price downplays the chances of shortages of food availability but concedes that prices would probably rise. "If you are suddenly operating on WTO rules (which impose tariffs on most agricultural products) then clearly there are going to be price increases in some goods and the extra demand for supplies from outside the EU will also push up prices."
There is another option to solve a potential food shortage - and one that some grocery executives think will be exercised if the UK looks like it could run out of food. "The soundings we are getting from government is that if we are facing disaster, we could simply extend Article 50 (the two-year Brexit stopwatch that started running when it was triggered in March 2017), said one.
Staying in the EU for a bit longer would keep the chiller cabinet full of sandwiches - but it would doubtless raise the political temperature.

An executive at Airbus says that work on the Galileo sat-nav system will have to be moved out of the UK if the company wins a key contract.
Galileo has become something of a political football in Brexit talks.
The EU says it would have to stop the UK from accessing the encrypted part of the network when it leaves next year.
Colin Paynter, the company's UK managing director, said that EU rules required Airbus to transfer all work to its factories in France and Germany.
Mr Paynter was speaking at a Commons committee hearing on Exiting the European Union on Wednesday.
The system was conceived to give Europe its own satellite-navigation capability - independent of US GPS - for use in positioning and timing applications, such as in finance, telecommunications, the utilities, and to support the emergency services and the military.
The UK has played a key role in the programme, and Airbus is currently bidding for the renewal of a contract covering the Galileo ground control segment - potentially worth about 200 million euros. This work is currently run out of Portsmouth.
About 100 people are currently employed by Airbus on these services. Most would likely have to move to where the work is, but it's possible some could be reallocated to other projects.
"One of the conditions in that bid documentation from the European Space Agency is that all work has to be led by an EU-based company by March '19," Mr Paynter told the committee.
"Effectively that means that for Airbus to bid and win that work, we will effectively novate (move) all of the work from the UK to our factories in France and Germany on day one of that contract."
Asked by Committee chair Hilary Benn MP whether the Brexit transition period could mitigate this condition, Mr Paynter replied: "No, because this area of Galileo - and many areas of Galileo - is classed as a security-sensitive procurement. I believe that isn't covered in the transitional arrangements."
The UK's access to Galileo's encrypted service, which would be required for military and security uses of the system, would be blocked by the EU after Brexit.
This warning prompted the Business Secretary Greg Clark to announce that the government would look into options for developing its own satellite-navigation system.
Asked by Labour MP Pat McFadden whether developing a British sat-nav system was feasible, Mr Paynter replied: "I think the key thing for me is, it's not up to industry to determine whether there's a requirement or need for an independent UK system... I would say that, in terms of feasibility, I think after such a long and deep involvement with the Galileo programme as UK industry, we have all the skills and capabilities needed to support that programme should it come out."
But Dr Bleddyn Bowen, who researches space and defence at the University of Leicester, told the committee: "Technically, yes, it's feasible - Britain could do it. But it will cost a lot of money and it will run over budget."
He added: "You need to look at the other GNSSs - global navigation satellite systems - that have been built. The Americans are currently building their third generation of GPS satellites, which have become notorious for cost overruns and delays because they're encountering new technological problems as they improve the system.
"Britain has just built the satellites for the Galileo system. That means Britain has to build a new satellite-navigation system - not the same one. That will mean new technological developments and innovations as well, which will cause delays."
According to one estimate, the UK has paid about 1.4 billion euros into the 12-14 billion-euro Galileo programme since 2005.
Estimates for the cost of an indigenous system in the range of £3-5bn were probably right, Mr Paynter said. That was money Dr Bowen told the committee could be better spent elsewhere, filling missing capability gaps in the British space programme.
Follow Paul on Twitter.

A post-Brexit UK-EU trade deal might take 10 years to finalise and still fail, the UK's top diplomat in Brussels has privately told the government.
The BBC understands Sir Ivan Rogers warned ministers that the European consensus was that a deal might not be done until the early to mid-2020s.
He also cautioned that an agreement could be rejected ultimately by other EU members' national parliaments.
PM Theresa May said she wanted Brexit to be "smooth and orderly".
In October, Sir Ivan, who conducted David Cameron's negotiation over the UK's relationship with the EU, advised ministers that the view of the 27 other countries was that a free trade agreement could take as long as a decade.
He said that even once concluded, the deal might not survive the process of ratification, which involves every country having to approve the deal in its own parliament.
It is also understood he suggested that the expectation among European leaders was that a free trade deal, rather than continued membership of the single market, was the likely option for the UK after Brexit.
Sir Ivan's private advice contrasts with ministers publicly insisting a deal can be done in the two years allowed by the triggering of Article 50 - the formal start of the process of leaving the EU.
Downing Street said he was relaying other EU members' views, rather than his own or the British government's.
A spokesman said: "It is wrong to suggest this was advice from our ambassador to the EU. Like all ambassadors, part of his role is to report the views of others."
Just how long will it take?
The government is intent on persuading us Brexit can be done smoothly, and to time.
So the suggestion that the UK's most senior diplomat in Brussels has privately told the government that a final trade deal with the rest of the EU might not be done for 10 years, and might ultimately fail, may give rise to more nerves.
EU leaders are meeting in Brussels - and will discuss Brexit negotiations at an end of summit dinner, without UK Prime Minister Theresa May being present.
Arriving in Brussels, Mrs May was asked about the 10-year claim, but concentrated her answer on the subject of immigration, which is what the EU leaders are focusing on during a chunk of their one-day summit.
She added that a smooth UK exit from the EU was "not just in our interests, it's in the interests of the the rest of Europe as well".
International Trade Minister Mark Garnier told the Commons Sir Ivan's views were "words from interlocutors" rather than a strict definition of how long talks will take.
Dominic Raab, a former minister and a Leave campaigner, told BBC Radio 4's Today programme that Sir Ivan was "scarred by his own pessimistic advice in the past".
"It's reasonable to set out the worst case scenario for a five to 10 year period to iron out a trade deal," he said.
"The key thing is whether we maintain barrier-free trade in the meantime in which case frankly there's no problem - we leave the EU in two years we complete the free trade agreement afterwards."
Former cabinet secretary Sir Gus O'Donnell predicted negotiating a final deal would take "at least five years".
"We certainly won't have come to any final arrangements in two years' time," he told BBC Radio 4's The Westminster Hour.
"We might well get to a point where we can symbolically leave but all sorts of details will still remain to be sorted out."
Remain-backing former Labour minister and European commissioner Lord Mandelson predicted "between five and 10 years" was the most likely timescale, telling a committee of MPs that after a deal is reached on the UK's exit terms, talks on trade arrangements would be harder and take longer.
Downing Street said Thursday's meeting showed the EU was facing up to the reality that the UK was leaving.
It is expected that the other members will discuss who will the lead the EU's negotiating team in Brexit talks.
This is expected to be former EU Commissioner Michel Barnier, who is in charge of the European Commission's Brexit team.
In other Brexit developments, the House of Lords EU financial affairs sub-committee has warned that financial services firms could quit the City of London unless there are transitional arrangements, or a "Brexit bridge" to prevent them moving to New York, Dublin, Frankfurt of Paris.
And European Parliament president Martin Schulz reiterated there would be no negotiation until the UK had officially notified the EU of its departure.
Addressing the 28 EU leaders, he added: "The UK and the EU are, and will remain, closely connected and there are too many lives on the line for an erratic, quick and total separation."
He urged leaders to work towards Brexit "in a spirit of loyal co-operation", adding: "We cannot allow the Brexit process to become an emotional affair, nor should we turn it into a legal maze from which exit is extremely difficult.
"We must not feed populists' unfounded claims that the EU is the master of all evil.  We must also use this moment to concretely reflect on what we want the EU to be in the future and to provide it with the necessary tools."

Detailed plans on the UK's post-Brexit future will not be published until after this month's EU summit.
Theresa May will summon senior ministers to an away day at Chequers in July to settle details of the white paper and find a common way forward.
With ministers aiming to complete the negotiations by October, many expected the plans to be released earlier.
Labour leader Jeremy Corbyn accused the Tories of "botching Brexit and risking jobs".
The announcement comes after Boris Johnson said the UK's Brexit strategy lacks "guts".
The white paper has been called the government's "most significant publication on the EU since the referendum".
Speaking at the G7 summit in Canada, the prime minister said: "There's going to be a lot of activity in the negotiations over the coming weeks.
One only has to look back at the turbulent week just passed to see the challenge Theresa May will face in uniting her bickering Cabinet at her away day.
It took several meetings with the Brexit Secretary David Davis on Wednesday to quell suggestions he'd resign in frustration with the current status of proposals.
Then a recording of the Foreign Secretary Boris Johnson emerged, undermining both the Prime Minister with claims the Brexit talks weren't going well, and also the pro-EU Chancellor Philip Hammond with a claim his Treasury Department was "the heart of remain."
The latter was more than just a limp lettuce leaf based gag (hearts of Romaine/heart of remain - ouch!) - it underlined the serious divisions now being so publicly displayed between senior ministers that would normally be hidden behind the closed doors of the cabinet.
Theresa May might hope taking them all away for a lock-in at Chequers will finally unite all factions behind a set of White Paper proposals - but this week suggests it won't be easy.
"I'll be going to the June European Council where we'll be talking about finalising the withdrawal agreement, but also pressing on the future relationship.
"After that, I'll be bringing my ministers together for an away day at Chequers to finalise the white paper we're going to be publishing.
"And then before Parliament breaks for the summer, we'll be bringing the Trade and Customs Bill back to the House of Commons.
"Throughout all of that time, the negotiations will be continuing."
In response, Mr Corbyn said that Parliament should take control and set negotiating priorities because the "divided and chaotic government" had failed.
"The government promised a 'detailed, ambitious and precise' Brexit White Paper this month setting out their negotiating priorities. Once again it's been postponed," he said,
"The Tories are botching Brexit and risking jobs and our economy in the process."
This week's events have once again highlighted the gulf of opinion in the cabinet over Brexit.
On Thursday, Mrs May was forced to agree to an "expected end date" of December 2021 for any interim arrangements after Brexit Secretary David Davis threatened to resign over the wording of the UK's proposed temporary customs agreement - the so-called backstop.
The proposal would see the UK match EU trade tariffs temporarily in order to avoid a hard Irish border post-Brexit.
That row was followed by comments from the Foreign Secretary Boris Johnson - recorded at a private dinner - where he warned of a Brexit meltdown, and said issues around the Irish border were mistakenly being allowed to dominate proceedings.
Mr Johnson also branded the Treasury - and, by implication, Chancellor Philip Hammond, "the heart of remain".
Responding to his comments, Mrs May said: "The foreign secretary has strong views on Brexit, but so do I. That's why I'm getting on with delivering Brexit."
But on Friday EU chief negotiator Michel Barnier criticised Mrs May's proposals for a customs arrangement.
He stressed that he was not rejecting the UK prime minister's ideas - but said any "backstop" to prevent a hard Irish border could not be time-limited.
Mr Barnier said the UK paper "raises more questions than it answers" but would be examined "objectively".
Mrs May told the BBC: "This is a negotiation, Michel Barnier has said exactly that point.
"We have put a proposal on the table, on this backstop relating to Northern Ireland, we will now sit down and negotiate it with the European Union."

Any "transitional deal" in the period after Brexit must end by June 2022, the time of the next general election, Philip Hammond has said.
But the chancellor said there must be "business as usual, life as normal" for Britons as the UK left the EU.
"Many things would look similar" the day after Brexit - on 29 March 2019 - as the UK moved gradually towards a new relationship with the EU, he said.
The EU has said it is too soon to discuss a transitional deal.
A European Commission spokesman said: "We are about to discuss the specifics of separation and once this is done to the satisfaction of everyone, we may move to the second step."
The UK is due to leave the EU at the end of March 2019 but there has been increasing talk of a "transitional" or "implementation" stage to smooth the process, before a new long-term relationship with the EU comes into force.
This could mean a period during which some EU rules would continue to apply to the UK after it has technically left the bloc. Newspaper reports have suggested these could include the free movement of people, something that was seen as a key issue in the vote to leave the EU.
Mr Hammond also appeared to acknowledge that it could mean new trade deals with non-EU countries could not be signed during that period.
The chancellor told BBC Radio 4's Today programme the length of any transitional deal would "be driven by technical considerations".
Beneath the surface, Chancellor Philip Hammond had been arguing for a transitional arrangement to avoid choppy waters in 2019. There is no longer any dissent in the ranks - that concept has been agreed by the Cabinet.
In return, the chancellor has acceded to demands by ministers who voted to leave the EU that any transitional phase must be completed by the scheduled date of the next general election - June 2022.
But have other disagreements so far escaped the political sonar?
On Thursday, immigration minister Brandon Lewis said it was a "simple matter of fact" that EU free movement rules would not apply after 2019.
Mr Hammond said this was correct because freedom of movement was an EU concept and the UK would leave the customs union and single market on 29 March 2019.
But he said the question that needed answering was what happened next, so that British people and businesses could "get on with their lives" without "massive disruption".
He said he hoped that, in the immediate aftermath, goods would "continue to flow across the border between the UK and the EU in much the same way as they do now".
On whether EU citizens would continue to be free to enter the UK, he said it would be "some time before we are able to introduce full migration controls between the UK and the European Union".
"That's not a matter of political choice, it's a matter of fact. We have to put in place quite a lot of new infrastructure, we will need a lot of new people, we will need new IT systems... This is going to take a while to deliver."
He said Britons wanted to know they would still be able to "go about their business" after March 2019, from buying European goods to going off on holiday, adding: "The government's job is to make sure that our economy can go on functioning normally, that people can go about their businesses as usual... that is our focus."
Some of Mr Hammond's colleagues who campaigned for a Leave vote have accepted that an "implementation period" after Brexit is likely.
The Conservative MP and Leave campaigner Nigel Evans said any transition period should end as soon as the UK had arrangements in place, saying: "This is not going to be seen as a ruse whereby some people who might have liked us to remain in the European Union can see this as an opportunity to keep us half in.
"That's not going to happen. We are, in all but one or two transitional arrangements, going to have left the European Union by March 2019."
Shadow Brexit secretary Sir Keir Starmer said Labour had been calling for "appropriate transitional arrangements" which the chancellor "now appears to accept".
"However, in light of the clear divisions this week within the Cabinet, I hope the chancellor was not merely speaking in a personal capacity," he said.
"I also hope that this is the final burial of the flawed proposition that 'no deal' is a viable option."
Lib Dem leader Sir Vince Cable said a transition period was only "kicking the can down the road".
"All the problems associated with a hard Brexit, leaving the single market, leaving the customs union, they will simply be confronted two years later."
Meanwhile, Malta's PM Joseph Muscat has said he is "starting to believe that Brexit will not happen", according to the Guardian.

It could take a further two years for Britain to fully leave the EU and start negotiating new trade deals with other countries, Liam Fox has said.
The international trade secretary told the BBC there could be a two-year "implementation phase" after the UK officially left the EU, in March 2019.
He had "no ideological barrier" to a phase to help business adjust, he said.
Mr Fox denied he was planning for a situation in which the UK left the EU without a deal.
It follows reports of cabinet divisions over Brexit, with Chancellor Philip Hammond saying last month that no deal with the EU "would be a very, very bad outcome".
If the UK leaves the EU without a trade agreement it could default to World Trade Organisation rules, potentially facing tariffs on goods and services traded with the EU.
Mr Fox said the UK could "of course survive with no deal" but he wanted a "full and comprehensive deal" with the EU.
He also said "the free trade agreement that we will have to come to with the European Union should be one of the easiest in human history" because the UK already met EU standards.
Some MPs have called for the UK to remain in the EU's single market and customs union after Brexit. Some non-EU European countries, such as Norway, are members of the single market.
Mr Fox said that he did not "have a problem" with a transitional Brexit deal, which he described as an "implementation phase" but insisted: "You can not leave the European Union and be in the single market and the customs union."
Speaking after a speech in Geneva, where he is meeting the WTO's director general, Mr Fox implied that such a phase could last two years.
Earlier this month, Mr Fox told Bloomberg TV he would be "very happy" with a transitional phase lasting "a few months".
He told the BBC: "We're going to leave [the EU] in March 2019.
"But if we can do it in a way that minimises or avoids any disruption to business, that provides them with the greatest amount of certainty and stability, then that's clearly a sensible thing to do.
"And if we have an implementation phase between us leaving the European Union and moving to whatever new arrangement and relationship we have with the EU,  I don't have any problem with that, for me there's no ideological barrier to that."
Mr Fox said he had been waiting to leave the EU "for a very long time, another two years, say, wouldn't be too much to ask".
And he said the UK would want to be able to "negotiate and conclude" trade deals outside the EU after March 2019 - but that was something that would be subject to negotiation.
BBC political editor Laura Kuenssberg said Mr Fox's apparent acceptance of "some kind of transition" indicated "a change in tone from Brexiteers" since the general election.
Lib Dem Brexit spokesman Tom Brake said: "I think the penny has finally dropped even with Liam Fox, that what the Brexiteers had presented as a simple, straightforward process that could be completed within a couple of years, now they realise that there's probably going to be a couple of years on top of that, and even that may be an underestimate."
Mr Fox's Labour shadow, Barry Gardiner, said any trade deal with the EU would have a political dimension.
Mr Gardiner said: "Liam Fox seems to be saying it makes economic sense for the EU to give us a good deal and we already have the basis for that, so why don't they just say, 'Right, we'll keep it as it is.'?
"But of course that ignores the fact that the European Union too has its own political objectives, and they are about ever-closer union of the remaining 27 and ensuring that nobody of those 27 feels that they too might get a better deal outside of Europe than inside."
Mr Fox also said earlier that the UK would take up an independent seat on the World Trade Organisation after Brexit and he believed that talks with the WTO indicated that "we will simply replicate our current obligations under the European Union as we move into the United Kingdom as an independent member".

Slowly but surely, like a submarine emerging from murky waters, the government's position on what happens immediately after Brexit is becoming clearer. And the speed of our withdrawal can now be measured, too.
Beneath the surface, Chancellor Philip Hammond had been arguing for a transitional arrangement to avoid choppy waters in 2019. There is no longer any dissent in the ranks - that concept has been agreed by the cabinet.
In return the chancellor has acceded to demands by ministers who voted to leave the EU that any transitional phase must be completed by the scheduled date of the next general election - June 2022.
But have other disagreements so far escaped the political sonar?
Mr Hammond privately believes a new trade deal with the EU simply can't be struck by the time of Brexit, in March 2019. So he would be prepared to leave things much as they are for a time.
While technically the UK would leave the single market and customs union, initially at least extremely similar arrangements would be put in place while a final free trade deal was completed. Then there would be a period where the new arrangements would be phased in.
That is why he uses phrases such as "transitional phase" or "transitional period". And on the record, he has said he wants to ensure things feel like "business as usual" to the British people, the day after the UK leaves.
But others in cabinet, not least Brexit Secretary David Davis, are much more confident that the essentials of any new trading arrangements with the EU could be hammered out by 2019.
So all that's needed isn't so much a "transitional phase" of further negotiation but an "implementation period" that puts any new arrangements in place.
For example, everyone recognises that, outside of the customs union, new staff and IT systems would be required to deliver the new regime and that simply couldn't be done the day after Brexit.
And there are further potential disagreements which could threaten the current esprit de corps - how long would the free movement of labour last after Brexit?
While, technically, free movement ends with EU membership, the government has already agreed there will be a "grace period" when EU citizens can still come to work here freely, so long as they register with the authorities.
A similar system operates in many EU countries now - and they call it "free movement".
The chancellor and Home Secretary Amber Rudd stress that it will take time to better police our borders, and to wean some companies off any over-reliance on migrant labour.
So the exact length of the grace period may yet end up in a graceless political dispute.
Terms of future trade could also cause conflict. Mr Hammond signalled his willingness to put any new trading arrangements with other countries on hold until after the transition.
Frankly the EU would probably demand this but it's hard to see Liam Fox, the international trade secretary, accept any ban on negotiating - rather than implementing - new deals until a transitional phase ends.
Then there is the thorny issue of which body supervises the trading rules between the UK and EU during a period of transition - would the European Court of Justice (ECJ) still have a role?
Mr Hammond has floated the idea of a tribunal, similar to the arrangements in place in European Economic Area countries such as Norway, to settle any disputes.
But if the EU insists on the ECJ, cabinet unity may yet fray. This might even torpedo any hope of a transitional arrangement that the British government could accept.
So while on the surface it may look like the course of HMS Brexit appears clearer, still waters run deep.

Airbus has warned that it could move wing-building out of the UK in the future if there is a no-deal Brexit.
The planemaker's chief executive, Tom Enders, said Airbus "will have to make potentially very harmful decisions for the UK" in the event of no deal.
He said it was a "disgrace" that firms could still not plan for Brexit.
His remarks were welcomed by Business Minister Richard Harrington, who said Airbus was correct to warn of the dangers of a no-deal scenario.
"Crashing out is a disaster for business," Mr Harrington told a meeting at the German embassy on Thursday morning.
"Airbus is correct to say it publicly about and I'm delighted they have done so," he added.
In all, Airbus employs 14,000 people in the UK.
That includes 6,000 jobs at its main wings factory at Broughton in Wales, as well as 3,000 at Filton, near Bristol, where wings are designed and supported.
Mr Enders said: "Please don't listen to the Brexiteers' madness which asserts that, because we have huge plants here, we will not move and we will always be here. They are wrong."
Responding to Airbus's statement, a government spokesperson said: "The UK is a world leader in aerospace. We are the home of the jet engine, the wing factory of the world and are world-renowned for our skills and capabilities in the most technically-advanced parts of aerospace manufacturing.
"It remains our top priority to leave the EU with a good deal; a deal that is good for business, will protect jobs and prosperity, and provide the certainty that business needs."
Airbus's latest intervention follows announcements by two other companies that they were moving their headquarters out of the UK.
Sony said it would transfer its European HQ from the UK to the Netherlands to avoid disruptions caused by Brexit.
And appliance maker Dyson announced it was moving its headquarters to Singapore, from Malmesbury in Wiltshire, although it said the decision had nothing to do with Brexit.
However, another firm, Japanese technology company Fujitsu, told the BBC it had "zero intention" of moving its operations out of London.
Duncan Tait, Fujitsu's European boss, said it had "a thriving business in the UK", adding: "We're recruiting people every week."
Mr Enders said that while the world's second-largest aerospace group could not "pick up and move our large UK factories to other parts of the world immediately", Airbus could be "forced to redirect future investments in the event of a no-deal Brexit".
"And make no mistake, there are plenty of countries out there who would love to build the wings for Airbus aircraft," he added.
"Brexit is threatening to destroy a century of development based on education, research and human capital."
Katherine Bennett, senior vice-president of Airbus in the UK, reinforced Mr Enders' message.
She told the BBC that a no-deal Brexit would be "catastrophic" for her business, with "chaos at the borders" that would hold up delivery of vital components.
This is not the first time that Airbus has warned of the consequences for its business of a no-deal Brexit.
Last year, it issued a risk assessment saying that if the UK left the EU without a withdrawal deal, it "would force Airbus to reconsider its investments in the UK and its long-term footprint in the country".
However, Mr Enders' latest remarks suggest that the firm has toughened its stance since then.
MPs are putting forward alternative plans to Theresa May's Brexit plan after it was voted down by Parliament last week.
The UK is due to leave the EU on 29 March this year.
by Theo Leggett, BBC business correspondent
The gloves are off. That's the clear message from Airbus' pugnacious chief executive, Tom Enders.
Opposition to Brexit from Airbus is not new. The company warned of the potential dangers to its business even before the referendum had taken place.
Since then, the rhetoric has been steadily ramped up. Last year, the company published a "Brexit Risk Assessment", in which it warned that leaving without a deal would be "catastrophic" for its business.
We've had warnings about the risk to future investment before, but now the threat is much more explicit and the language is much more forthright. The failure to come up with a clear plan is a "disgrace". Other countries would "love" to build the aircraft wings currently made at Broughton.
There's even a warning not to listen to "the Brexiteers' madness". The time for diplomacy, it seems, is past.
So what's changed? The company clearly believes that the risk of "no deal" is growing, thanks to the impasse in the House of Commons.
And as a business which relies on the rapid transfer of parts from the UK to assembly lines in France and Germany, it is very exposed to any delays in shipments - or problems getting new safety certification.
Meanwhile, Tom Enders is due to leave his job in April. So perhaps he's in a very good position to talk tough, without worrying whom he's upsetting in the process.

Voting to leave the European Union was a "bad decision" for the UK, the Irish foreign minister has said.
Charlie Flanagan said Brexit could be "painful" for the UK and his country, which he added should not be "placed in a position of more disadvantage".
He also urged negotiators to keep the Common Travel Area between Northern Ireland and the Republic.
The comments come after Prime Minister Theresa May met European Council President Donald Tusk in London.
Mr Flanagan told BBC's Newsnight it was "absolutely essential" there was no return to a hard border on the island of Ireland - which is expected to be a key element of Brexit negotiations between the UK and EU.
"The Good Friday Agreement remains the foundation stone of our peace, and anything adverse to that agreement will not be acceptable," he said.
However, despite his criticism of the decision to leave, the Irish minister said he believed there was no intent to punish Britain among EU members, adding that the relationship between the UK and the Republic of Ireland was its "warmest ever".
He said: "I believe [Brexit] was a bad decision, but of course as a democrat I fully respect and recognise the will and wishes of the British people. We've got to deal with that now.
"The Article 50 process has commenced, and I believe it's essential now that we get through the negotiations in such a way that the end result can be as close as possible a relationship between the European Union and the United Kingdom, albeit with the UK gone."
On Friday, Mrs May and Mr Tusk met at 10 Downing Street for the first time since Article 50 was triggered, with Gibraltar at the heart of the talks.
In its draft negotiating guidelines, published last week, the EU said decisions affecting Gibraltar - a UK overseas territory - would have to be taken with the agreement of the Spanish government.
This led to former Conservative leader Lord Howard saying the prime minister would defend Gibraltar in the same way Margaret Thatcher defended the Falkland Islands.
Mrs May laughed off the prospect of war with Spain, but after her meeting with Mr Tusk, a Number 10 spokesman said she had been clear she was determined to achieve the "best possible deal" for Gibraltar as well as the UK.
"The PM also made clear that... there would be no negotiation on the sovereignty of Gibraltar without the consent of its people," he added.
EU sources told the Press Association it had been a "good and friendly" meeting.
One source added: "They agreed to stay in regular contact throughout the Brexit process to keep a constructive approach and seek to lower tensions that may arise, also when talks on some issues like Gibraltar inevitably will become difficult."

MPs have overwhelmingly agreed to let the government begin the UK's departure from the EU as they voted for the Brexit bill.
The draft legislation was approved by 494 votes to 122, and now moves to the House of Lords.
Shadow business secretary Clive Lewis was one of 52 Labour MPs to defy party orders to back the bill and he resigned from the front bench.
PM Theresa May wants to trigger formal Brexit talks by the end of March.
She will do this by invoking Article 50 of the Lisbon Treaty, but requires Parliament's permission before doing so.
Mr Lewis, who earlier said he was undecided on whether to support the European Union (Notification of Withdrawal) Bill, announced his resignation as MPs began voting for the final time.
He said he "cannot, in all good conscience, vote for something I believe will ultimately harm the city I have the honour to represent, love and call home".
Leader Jeremy Corbyn said he understood the difficulties the vote presented some of his MPs but said they had been ordered to back the Article 50 because the party would not "block Brexit".
Shadow home secretary Diane Abbott, who missed last week's initial vote on the bill, backed it this time.
She told the BBC she had "a lot of misgivings about the idea of a Tory Brexit" and predicted the UK would "come to regret it", but added: "I'm a loyal member of the shadow cabinet and I'm loyal to Jeremy Corbyn."
The Labour rebellion was five MPs up on last week's vote, while former Chancellor Ken Clarke was again the only Conservative to vote against the two-clause bill.
During the voting, SNP MPs were reprimanded by deputy speaker Lindsay Hoyle after they started singing Ode to Joy, the European Union anthem.
Afterwards, Brexit Secretary David Davis hailed the "historic vote", adding: "It is now time for everyone, whichever way they voted in the referendum, to unite to make a success of the important task at hand for our country."
Peers will now consider the draft legislation, and a government source told BBC political editor Laura Kuenssberg: "If the Lords don't want to face an overwhelming public call to be abolished they must get on and protect democracy and pass this bill."
Earlier the bill survived several attempts to change its wording and add extra conditions.
These included Labour MP Harriet Harman's bid to protect the residence rights of EU citizens in the UK, which was outvoted by 332 votes to 290, with three Conservative MPs rebelling.
A Liberal Democrat bid for a referendum on the terms of the UK leaving the EU was defeated by 340 votes to 33.
Afterwards, Mr Corbyn tweeted: "Real fight starts now. Over next two years Labour will use every opportunity to ensure Brexit protects jobs, living standards and the economy."
But Scottish First Minister Nicola Sturgeon accused him of giving the Conservatives a "blank cheque".
She tweeted: "You didn't win a single concession but still voted for the bill. Pathetic."
The bill will be debated in the House of Lords after it returns from recess on 20 February.
Liberal Democrat leader Tim Farron vowed the party's peers would seek to amend the bill in the Lords, including another attempt to ensure a referendum on the final Brexit deal.

European Council President Donald Tusk has hinted that the UK should stay in the EU, after the prime minister's Brexit deal was rejected in parliament.
"If a deal is impossible, and no-one wants no deal, then who will finally have the courage to say what the only positive solution is?" he tweeted.
MPs voted by 432 votes to 202 to reject the deal, which sets out the terms of Britain's exit from the EU on 29 March.
Other EU officials and politicians reacted with dismay to the result.
It was the largest defeat for a sitting government in history, with 118 of the votes against coming from Prime Minister Theresa May's own Conservative Party.
It has cast more doubt on the Brexit process, and the leader of the opposition Labour Party, Jeremy Corbyn, has tabled a vote of no confidence in the government.
As well as Mr Tusk's tweet, there has been plenty of comment on Tuesday's vote from across Europe. Here are the key quotes:
European Commission President Jean-Claude Juncker warned that time was running out for the UK to strike a deal.
"I urge the United Kingdom to clarify its intentions as soon as possible. Time is almost up," he said shortly after the result was announced.
"The risk of a disorderly withdrawal of the United Kingdom has increased with this evening's vote," he added.
The EU's chief Brexit negotiator Michel Barnier said he "profoundly" regretted the vote.
"An orderly withdrawal will remain our absolute priority in the coming weeks," he told the European Parliament in Strasbourg.
He added that there would be a favourable response if Mrs May were prepared to rethink her position on issues like the single market and customs union.
Chancellor Angela Merkel said there was still time to negotiate but "we're now waiting on what the prime minister proposes".
Finance Minister and Vice Chancellor Olaf Scholz said Tuesday was a "bitter day for Europe".
"We are well prepared, but a hard Brexit would be the least attractive choice, for the EU and [UK]," he said.
Annegret Kramp-Karrenbauer, the leader of the ruling Christian Democrat Union party, echoed this view.
"A hard Brexit will be the worst of all options," she said.
"The pressure is mainly on them," French President Emmanuel Macron said of the UK.
He said a transition period was essential because a no-deal Brexit would be damaging.
"We will have to negotiate a transition period with them because the British cannot afford to no longer have planes taking off or landing at home," he said.
Later a presidential source said France was stepping up preparations for a "no-deal" Brexit.
Prime Minister Leo Varadkar said that the Republic was also now preparing for a no-deal Brexit but would work hard to avoid it because it "would not protect the peace in Northern Ireland".
But he said the ball was now in the UK government's court to find a solution.
"We understand the PM will now consult with other parties and other political leaders on an agreed way forward we welcome that," he said.
"The onus is on Westminster to come up with solutions that they can support but they must be solutions that the European Union and Ireland can accept."
Meanwhile Foreign Minister Simon Coveney ruled out any alternative to the agreement reached with the UK over the Irish border.
"We're not going to allow physical border infrastructure to reappear," he told national broadcaster RTE.

The government has survived an attempt by pro-EU Conservative MPs to change its post-Brexit trade strategy.
The MPs wanted the UK to join a customs union if it does not agree a free-trade deal with the EU.
But the government, which says a customs union would stop it striking new trade deals, won by 307 to 301.
Ahead of the vote, Tory MPs were told a defeat would lead to a vote of no confidence in the government, sources told the BBC's John Pienaar.
The government did, however, lose a separate vote on its Trade Bill on the regulation of medicines after Brexit.
MPs backed an amendment by 305 votes to 301 that would keep the UK in the European medicines regulatory network.
There were 12 Tory rebels in both the customs and medicines votes - but the government's total was boosted by four Labour MPs in the customs vote.
The customs union allows for tariff-free trading between members with a common tariff set for imports from the rest of the world.
The UK is due to leave the EU on 29 March 2019 but the two sides have yet to agree how their final trading relationship will work.
The Commons has been debating two pieces of legislation - on customs and trade - and there have been several attempts to change them by both pro-Brexit and pro-EU MPs.
The latest key vote was on customs, with a debate sparked by Tory MP Stephen Hammond's amendment to the Trade Bill.
It stated that if a free trade area had not been negotiated by 21 January, ministers must change tack and start discussions on joining a customs union.
Labour backs the idea of a customs union with the EU after Brexit - but the government says this would mean the UK is unable to strike its own international trade deals.
During the debate on the Trade Bill, a minister tried to persuade Mr Hammond and his supporters to back down, promising to deal with the "essence" of their concerns when the bill goes to the House of Lords.
Although this was rejected by Mr Hammond, the government won the vote and the bill was later approved by the House of Commons.
The 12 MPs that voted against the government on customs and trade were: Heidi Allan, Guto Bebb, Ken Clarke, Jonathan Djanogly, Dominic Grieve, Stephen Hammond, Philip Lee, Nicky Morgan, Bob Neill, Antoinette Sandbach, Anna Soubry and Sarah Wollaston.
On the other side, four Labour MPs voted with the government: Frank Field, Kate Hoey, John Mann, and Graham Stringer.
Lib Dem leader Sir Vince Cable and his predecessor Tim Farron - who were criticised after missing Monday night's knife-edge Brexit votes - were back at Westminster and voted against the government.
But a former Lib Dem minister, Jo Swinson, complained that Tory MP Brandon Lewis participated in the votes despite having agreed to abstain.
Ms Swinson, a Remain supporter who has recently given birth and was unable to vote, tweeted Mr Lewis did not keep to their arrangement to balance out her effective abstention - known as "pairing" - and accused the government of "desperate stuff".
They didn't escape defeat for long.
Having squeaked through last night the government was beaten for only the second time ever in the Commons on key Brexit legislation.
And guess what, it was on a vote they didn't expect to lose - Dr Phillip Lee, who quit the government to speak out on Brexit, put forward his own amendment to protect the links between the UK and the European Medicines Agency to ensure the smooth flow of medicines and new drugs for British patients after Brexit.
And he had enough to support to win it, just. An embarrassment for the government certainly.
It is another reminder of how difficult it is for Theresa May to get her way in the House of Commons where she doesn't have her own majority.
It is serious. A defeat is a problem. But it wasn't a complete disaster tonight for two reasons.
First, the amendment isn't a million miles away from the government's own policy. While not straightforward, the vote hasn't forced a screeching U-turn.
The more important reason is that the vote that followed, on keeping the UK in a customs union, went the other way.
Read Laura's blog
The vote on medicine regulation was only the government's second defeat on Brexit in the House of Commons.
MPs voted for the UK to take "all necessary steps" to participate in the regulatory network operated by the European Medicines Agency after it leaves the EU.
The agency, which evaluates and supervises medicines and helps national authorities authorise the sale of drugs across the EU, is currently based in London but is moving to Amsterdam after Brexit.
There have been warnings that Brexit may cause delays in UK patients getting new drugs.
The government says it is "seeking participation" in the agency after Brexit and would make an "appropriate financial contribution" in return.
But it has not agreed to take "all necessary steps" to secure this.
Responding to the defeat, the government said: "We will now reflect on this amendment and seek to revisit in the Lords."

Michael Gove has warned of the rise of identity politics in Britain, but insisted the Brexit campaign which he helped lead did not fan its flames.
The Tory minister said elements on the left and right wanted to pit groups against each other in a "conflict for recognition, rights and resources".
But he rejected claims Leave voters were also examples of "identitarians".
He told an event in London that Brexit was motivated by a desire to "restore faith in our democratic institutions".
Addressing a conference on the future of the United Kingdom, the environment secretary said the tendency to look at "political questions through the prism of identity" posed a challenge not just to the constitutional order which he said had, for the most part, served the UK so well for hundreds of years but to the concept of individual rights.
"The identitarians want to move away from the liberal principles of equal treatment for all, colour blindness and respect for individual rights," he told the event, hosted by the Policy Exchange think tank.
"Instead they embrace a politics which divides society in contending groups and demands people define themselves by their group membership rather than as autonomous individuals."
On the left of politics, he said this was characterised by an "insistence that an individual should check their privilege before speaking and pipe down if they don't fit in or avoid cultural appropriation - in other words know their place in the world if they want to get a hearing".
Despite the "effective eclipse of UKIP" as a political force, he said the manifestation of identity politics on the right of the political spectrum in the UK and further afield was "equally concerning".
"You hear it when there is an appeal to defend men's rights which is an attempt to make gender a cause of conflict, not an aspect of character," he said.
"Or when some politicians claim our borders should be closed to people because of their faith or religion."
In contrast, he said unionism as a political tradition, while needing to be rejuvenated and kept relevant, was underpinned by principles and institutions which offered a "warm home" to "so many from a distinct and diverse background".
Through its allegiances to "Magna Cartas, Bills of Rights, Great Reform Acts and Golden Jubilees, not tribal, cultural, sexual and divisive totems" - unionism stood in direct opposition to identity politics, he added.
Accusing the SNP of "playing with" identity politics for its own electoral benefit and using Brexit as just one of many "grievances", he said Scottish nationalism "conflates truly progressive politics with superior virtue that can apparently only really come from living north of the border".
But Mr Gove came under fire from former Conservative MP and Lib Dem MSP Keith Raffan who said the Brexit vote, opposed by 62% of those who voted in Scotland, had put a "totally avoidable" strain on the union, as demonstrated by the Scottish Parliament's recent refusal to give its consent to the EU Withdrawal Bill.
Vote Leave's campaign claims about Turkish immigration were "far worse" than anything the SNP had ever come up with, he suggested.
"Haven't you played with identity politics when the Leave campaign stated that 80 million Turks could decamp to England - dog-whistle politics of the nastiest kind," he asked Mr Gove.
The environment secretary, who is Scottish, said he "respectfully disagreed" with claims the Brexit vote was driven by xenophobia or a nostalgia for a return to the the time when Britain was an imperial power.
"People wanted to make sure they had control of their borders, of our taxes, of our laws and all of that was part of a broad campaign to restore faith in our democratic institutions," he said.
Asked directly whether Leave supporters were identitarians, Mr Gove said the "answer to that question is no".
Speaking at the same event, Conservative Party chairman Brandon Lewis said English identity should be celebrated more openly as part of the UK projecting an "outward-looking" face to the world after Brexit.
But former Labour cabinet minister Jim Murphy said that while he remained a passionate believer in the union, he feared David Cameron's efforts to make the Conservatives a truly national party had "dissipated" in favour of them embracing a narrower English nationalism.
And the SNP's Pete Wishart poured scorn on the whole idea of an "unionism convention" as well as Mr Gove's claim that the UK had become "more welcoming" to immigrants since the Brexit vote. He tweeted:

MPs have again failed to agree on proposals for the next steps in the Brexit process.
The Commons voted on four alternatives to Theresa May's withdrawal deal, but none gained a majority. One Tory MP resigned the whip in frustration.
Mrs May will now hold a crucial cabinet meeting to decide what to do and whether to put her deal to MPs again.
The UK has until 12 April to either seek a longer extension from the EU or decide to leave without a deal.
The so-called indicative votes on Monday night were not legally binding, so the government would not have been forced to adopt the proposals. But they had been billed as the moment when Parliament might finally compromise.
Mrs May's plan for the UK's departure has been rejected by MPs three times.
As a result of that failure, she was forced to ask the EU to agree to postpone Brexit from the original date of 29 March.
Meanwhile, Parliament took control of the process away from the government in order to hold a series of votes designed to find an alternative way forward.
Last week, eight options were put to MPs, but none was able to command a majority, and on Monday night, a whittled down four were rejected too. They were:
Those pushing for a customs union argued that their option was defeated by the narrowest margin, only three votes.
It would see the UK remain in the same system of tariffs - taxes - on goods as the rest of the EU - potentially simplifying the issue of the Northern Ireland border, but preventing the UK from striking independent trade deals with other countries.
Those in favour of another EU referendum pointed out that the motion calling for that option received the most votes in favour, totalling 280.
Following the failure of his own motion, Common Market 2.0, Conservative former minister Nick Boles resigned from the party.
The MP for Grantham and Stamford said he could "no longer sit for this party", adding: "I have done everything I can to find a compromise."
As he left the Commons, MPs were heard shouting, "don't go Nick", while some MPs from other parties applauded him.
He later tweeted that he would remain an MP and sit in the Commons as "an Independent Progressive Conservative".
Brexit Secretary Stephen Barclay said the "only option" left now was to find a way forward that allows the UK to leave the EU with a deal - and the only deal available was the prime minister's.
If that could be done this week, he added, the UK could avoid having to take part in elections to the European Parliament in May.
Health Secretary Matt Hancock agreed it was time for Mrs May's deal to be passed.
But Labour leader Jeremy Corbyn said that while it was "disappointing" that none of the proposals secured a majority, he said he wanted to remind the Commons that Mrs May's deal had been "overwhelmingly rejected".
He urged MPs to hold a third round of indicative votes on Wednesday in the hope that a majority could yet be found for a way forward.
For months, Parliament has been saying "Let us have a say, let us find the way forward," but in the end they couldn't quite do it. Parliament doesn't know what it wants and we still have lots of different tribes and factions who aren't willing to make peace.
That means that by the day, two things are becoming more likely. One, leaving the EU without a deal. And two, a general election, because we're at an impasse.
One person who doesn't think that would be a good idea is former foreign secretary and Brexiteer Boris Johnson.
He told me going to the polls would "solve nothing" and would "just infuriate people". He also said that only somebody who "really believes in Brexit" should be in charge once Theresa May steps down. I wonder who that could be...
Hear more from Laura and the gang in Brexitcast.
Liberal Democrat Norman Lamb told BBC Look East he was "ashamed to be a member of this Parliament" and hit out at MPs in his own party - five of whom voted against a customs union and four of whom voted against Common Market 2.0.
He said the Commons was "playing with fire and will unleash dark forces unless we learn to compromise".
But prominent Brexiteer Steve Baker said he was "glad the House of Commons has concluded nothing".
He said the prime minister must now go back to the EU and persuade them to rewrite the withdrawal deal - something they have so far refused to do - otherwise the choice was between no deal or no Brexit.
Senior figures in the EU, though, showed their frustration at the latest moves in Westminster.
European Parliament Brexit coordinator Guy Verhofstadt tweeted that by voting down all the options, a "hard Brexit becomes nearly inevitable".
BBC Europe editor Kayta Adler said the mood in Brussels was one of disbelief - that the UK still does not seem to know what it wants.
She said EU leaders were also questioning the logic of arguing over things like a customs union or Common Market option at this stage, because right now, the UK has only three options as they see it - no deal, no Brexit or Theresa May's deal - and anything else is a matter for future talks once the UK has actually left.

It was only yesterday that the Brexit Secretary, David Davis, told MPs it just might all be a bit tricky to have a White Paper, a formal document outlining the government's plans for Brexit, and stick to the timetable they want to pursue.
Rebel Remainers though were "delighted", that, stealing Jeremy Corbyn's thunder, a planted question from a loyal Tory MP at PMQs today produced in fact a promise from the Prime Minister that, after all, there will be a White Paper.
It is a climbdown, no question, a last-minute change of heart.
Late last night Brexiteers were being assured there would be no bending, no delay to the government's plans and no giving in to the Remainers.
Even early this morning, government sources were privately suggesting that they were quite happy to have the white paper option up their sleeve, but there were no immediate plans to make that promise.
Then voila, at 1205 GMT, the pledge of a white paper suddenly emerged. As one senior Tory joked, "welcome to the vacillation of the next two years".
It may be being described as a "massive, unplanned" concession but it doesn't seriously hurt the government.
First off, it shows goodwill to the rebel Tory Remainers, many of whom feel their Eurosceptic rivals have had the upper hand of late. Schmoozing matters round these parts.
It takes one of the potential arguments that could have gathered pace off the table, before the Article 50 bill is even published. And, rightly or wrongly, no one expects a white paper will contain anything new that the prime minister has not yet already said.
It's largely a victory for the Remainers about process, rather than substance.
For her critics this is evidence of weakness, that's she has been pushed into changing her mind.
But it doesn't need to change the government's timetable, and today's embarrassment of a climbdown might be worth the goodwill that Number 10 will get in return.

Tony Blair has warned Jeremy Corbyn that Brexit will make it harder for Labour to deliver its promises if it wins power.
The former prime minister said Mr Corbyn would be in "exactly the same position" as the Tories  - distracted by Brexit and short of money.
Speaking to the BBC's John Pienaar, he defended his call for a second EU referendum.
Labour has backed Brexit and ruled out a second referendum if it wins power.
One member of Labour's shadow cabinet told the BBC Mr Blair's intervention was "utterly unhelpful".
"Lots of Labour voters voted for Brexit and this to them sounds like the metropolitan elite ignoring them," he said.
"The whole Tony Blair project was about being on the right side of public opinion. And now look at this. Are you telling me the Tony Blair of 1994 would have said this?"
Britain is due to leave the EU on 29 March 2019, but Mr Blair said it would be too late to change course by then.
He has repeatedly argued that people are entitled to change their mind - either through another referendum or a general election - once the terms of its departure are clear.
And he urged the current Labour leadership to adopt the same stance.
The former prime minister said he was "committed" to seeing a Labour government elected, but added a "qualification" - which was that "it's going to be extremely difficult in my view for Labour to deliver on its promises if it puts itself in exactly the same position as the Tory government's going to be on Brexit - because it will find it has less money to deal with the country's problems, that it's distracted by dealing with Brexit rather than the health service, jobs and living standards."
The UK would "face a very challenging situation" if it was leaving the EU under a Corbyn government, he added.
Mr Blair said that if people voted again for Brexit, he would not push for a third poll - "that concludes the argument", he said.
But he said that he would not support either of what he saw as the two most likely outcomes of negotiations - a Canada-style free trade deal or the UK being aligned with the EU but having no influence over key decisions.
Shadow Brexit secretary Sir Keir Starmer says Labour will push for a deal that would preserve as many of the benefits of the single market and customs union as possible, as well as protecting workers' rights and the environment.
But Mr Blair believes this is a "confusing" strategy and is not "credible".
"Far better to fight for the right for the country to re-think, demand that we know the full details of the new relationship before we quit the old one, go to the high ground on opposing Brexit and go after the Tories for their failures to tackle the country's real challenges.
"Make Brexit the Tory Brexit. Make them own it 100%. Show people why Brexit isn't, and never was, the answer."
Mr Blair - a longstanding critic of Labour leader Jeremy Corbyn - has ditched his business interests to take a more active role in British politics through his Institute for Global Change think tank.
He has previously attacked Mr Corbyn's stance on Brexit - prompting the Labour leader to say Mr Blair should respect the result of the 2016 EU referendum.
Richard Tice, co-chairman of the pro-Brexit Leave Means Leave campaign, said Mr Blair "and his elite gang" were "still determined to stop Brexit" and will lead the UK "to the very bad deal which we had in the single market and the customs union".
In Mr Blair's latest article published on his institute's website, he offered this advice to Jeremy Corbyn and his team: "At every PMQs nail each myth of the Brexit campaign, say why the Tory divisions are weakening our country, something only credible if we are opposed to Brexit, not advocating a different Brexit, and challenge the whole farce head on of a prime minister leading our nation in a direction which even today she can't bring herself to say she would vote for.
"If we do leave Europe, the governing mind will have been that of the Tory right.
"But, if Labour continues to go along with Brexit and insists on leaving the single market, the handmaiden of Brexit will have been the timidity of Labour."
Mr Blair's comments came as his institute issued a document highlighting developments in the UK since the Brexit vote, including a downgrade in economic forecasts.

"Are you trying to provoke the UK government?" was my question today to Michel Barnier, the EU's chief Brexit negotiator.
His favourite maxim is "stay calm and keep negotiating" but, I put it to him, he was surely well aware of the explosive reaction that would probably follow in the UK after seeing the European Commission's protocol on the Irish border.
So was this an EU ruse to rouse the UK government into focusing on and speeding up negotiations? After all, Mr Barnier never tires of pointing out that the time to negotiate is running out.
No, he told me. His aim was not to provoke or to create shockwaves. He wanted to make these negotiations a success. But, he added, he had long warned the UK that leaving the EU would have serious consequences.
The commission's proposal for Northern Ireland appeared today as part of its draft UK withdrawal agreement.
This is the European Commission's interpretation - in legally binding language - of the agreements it believes have so far been reached with the UK government. They include the so-called Brexit Bill and the rights of EU citizens in the UK and UK citizens in the EU after Brexit, and separately outline issues the commission still wants to be negotiated.
No final agreement has yet been reached on the Irish border conundrum and the fudged compromise settled on just before Christmas became painfully exposed on Wednesday.
Both the EU and the UK say they are committed to safeguarding the Good Friday Agreement and avoiding the re-introduction of a hard border between Northern Ireland and the Irish Republic.
The UK believes this can be done as part of an eventual far-reaching free trade agreement with the EU and with the help of smart technology.
These are known as options A and B on Ireland.
The EU has insisted - and the UK agreed back in December - on an option C as a fallback plan.
This would see full regulatory alignment between Northern Ireland and the EU in areas necessary to maintain North-South cross border co-operation.
In the absence to date of any concrete detail from the UK on how options A or B would work, the European Commission has gone to town in this draft withdrawal agreement on option C - including Northern Ireland staying in an EU customs union and in relevant parts of the single market, all under the jurisdiction of the European Court of Justice.
Michel Barnier insisted it was the EU's duty to ensure the integrity of the Good Friday Peace Agreement after Brexit, but you couldn't have crossed more UK lines if you'd tried.
And, right on cue, all the main actors delivered the lines you would expect.
Theresa May rejected the commission's text, vigorously defending the territorial integrity of the UK. She is mindful of course of the strong opinion of Northern Ireland's Democratic Unionist Party (DUP), which she relies on for support in the UK parliament.
Michel Barnier, meanwhile, defended the position of EU member state Ireland.
But before you go away, head in hands, thinking: we're in another deep Brexit crisis - we are actually slap back in the middle of a negotiation.
There were strong words but no-one slammed any doors today.
The commission's draft text will now be debated and possibly amended by the 27 EU member states before then being presented to the UK government for negotiation.
In the next stage of this drama Donald Tusk, the President of the European Council, heads to London to see the prime minister ahead of her Brexit speech on Friday.
The EU says it will be listening closely.
And as a parting shot on Wednesday - in an apparent spirit of compromise even if on a separate Brexit subject - the UK has offered a step towards more rights for EU citizens coming to the UK during the transition.
Still, as one EU diplomat pointed out to me soberly, be under no illusion, the Irish question still has the potential to bring the whole Brexit deal tumbling down.

Downing Street has reassured fans of Strictly Come Dancing that the show is not at risk from Brexit, following claims by Sir Vince Cable.
Sir Vince - who appeared on the the Strictly Christmas special in 2010 - said a "cack-handed" immigration policy could stop dancers from the EU appearing on the show.
The Lib Dem leader made the comments after a meeting with Michel Barnier.
He made the case for a second referendum to the EU negotiator.
Many of the professional dancers on Strictly Come Dancing come from EU countries.
"As British society falls apart it could pose a risk to Strictly,"  Sir Vince, who has said he wants to halt Brexit, told The Telegraph.
"If we have a cack-handed immigration policy like what we have for non-EU citizens, all kinds of perverse decisions could be made,"
But a Downing Street spokesperson said: "I think Strictly will be fine."
The government has faced calls from dance companies, the Musicians' Union and other arts organisations to protect the free movement of performers when the UK leaves the EU in March.
Launched by the BBC in 2004, Strictly Come Dancing has become a firm Saturday night favourite and is currently in its 16th series.

Brexit's fate is "in the hands of our British friends" after EU leaders agreed to delay the departure date by at least two weeks, says Donald Tusk.
If MPs approve Theresa May's withdrawal deal next week, Brexit would be delayed from 29 March until 22 May.
But if they do not, the UK has until 12 April to come up with a new plan.
European Council President Mr Tusk said that until 12 April, "anything is possible" including a much longer delay or cancelling Brexit altogether.
Speaking in Brussels on Friday, he said he was "really happy" the 27 EU leaders had reached a unanimous decision to extend the two-year Article 50 process, under which the UK was due to leave the EU next Friday.
"It means that until 12 April, anything is possible: a deal, a long extension if the United Kingdom decided to rethink its strategy, or revoking Article 50, which is a prerogative of the UK government.
"The fate of Brexit is in the hands of our British friends. As the EU, we are prepared for the worst, but hope for the best. As you know, hope dies last."
According to the final summit conclusions, the UK is expected to "indicate a way forward" before 12 April, if MPs do not approve the withdrawal deal negotiated with the EU, which would then be considered by the European Council.
Theresa May has been granted a little breathing space. The EU has allowed a few more days to try to get her deal through the House of Commons.
But it's not the timetable that she chose.
And as things stand, the expectation that the compromise deal will get through is low.
And, more to the point, the government does not believe that it can hold off another attempt by a powerful cross-party group of MPs who are resolved to put Parliament forcibly in charge of the process to find alternatives.
Ministers are therefore today not just wondering about how to manage one last heave for the prime minister's deal, but what they should do next, when - odds on - the whole issue is in the hands of the Commons, not Number 10.
Read Laura's blog
The UK must decide by then whether it will be taking part in European Parliamentary elections from 23-26 May - if it does not, then a long delay would become "impossible", Mr Tusk said.
On Friday, Mrs May's deputy David Lidington met opposition parties to discuss how MPs could vote on alternatives to the government's Brexit plan next week.
These could include options such as holding another referendum, leaving with no deal or pursuing a closer economic arrangement such as the "Common Market 2.0" plan.
MPs are expected to vote on Mrs May's deal for a third time next week, despite Commons Speaker John Bercow ruling that it could not be brought back for another vote without "substantial" changes.
But in a letter to all MPs on Friday evening, Mrs May said it was possible a third vote on the deal may not take place "if it appears there is not sufficient support to bring the deal back next week".
The prime minister offered to talk to MPs over the coming days "as Parliament prepares to take momentous decisions".
She also referred to her televised address on Wednesday, in which she blamed the delay to Brexit on MPs.
Mrs May acknowledged that "a number of colleagues had raised concerns" about her words and it had not been her intention to make a their "difficult job... any more difficult".
Earlier, Business Secretary Greg Clark told the BBC that if they do not back Mrs May's deal, then the government would give Parliament the means to express their views on a series of other options.
He said this meant an attempt by a cross-party group to enable MPs to take control of Commons business, so they can get indicative votes, would not be necessary.
But he said the government's ambition should be to try to build as big a consensus as possible on Brexit, rather than simply "getting it over the line" with a slim majority of one or two votes.
29 March: Current Brexit date in UK law
12 April: If MPs do not approve the withdrawal deal next week - "all options will remain open" until this date. The UK must propose a way forward before this date for consideration by EU leaders
22 May: If MPs do approve the deal next week, Brexit will be delayed until this date
23-26 May: European Parliamentary elections are held across member states
Mrs May has ruled out revoking Article 50, which would cancel Brexit, and has said it would be wrong to ask Britons to vote for candidates for the elections to the European Parliament, due to be held from 23-26 May, three years after they voted to leave the EU.
Her official spokesman said: "There is now a clear point of decision. If we are able to have a successful vote next week then we can pass the necessary legislation for ratifying the agreement and we can, as a country, be outside the European Union two months today."
For now, the UK's departure date is still written in to law as next Friday, 29 March.
But Mrs May is expected to change that by tabling legislation next week and getting it through the Commons and the Lords.
The withdrawal deal sets out the terms of the UK's departure from the bloc, including the "divorce bill", the transition period, citizens' rights and the controversial "backstop" arrangements, aimed at preventing a return to border checks between Northern Ireland and the Republic of Ireland.
But it must be approved by UK MPs, who have already rejected it twice by large margins.
The Irish premier Leo Varadkar said the choices were now obvious: "It's this agreement, no deal, or the parliament taking indicative votes for a much closer long-term relationship with the EU."
But Nigel Dodds, deputy leader of the DUP - whose votes Mrs May relies on to support her minority government - said the prime minister had "missed an opportunity" to propose changes to the withdrawal agreement to help get it through the Commons.
"The prime minister has now agreed with the EU to kick the can down the road for another two weeks and humiliatingly revoke her oft-stated pledge that the UK would leave the EU on 29 March," he said.
"Nothing has changed as far as the withdrawal agreement is concerned."

"The ball is in the government's court" when it comes to a way forward with Brexit, Labour's Sir Keir Starmer says.
Talks between Labour and the government began last week, with Theresa May saying only a cross-party pact would see MPs agree a deal in Parliament.
But the shadow Brexit secretary said Mrs May's team had "not changed its position" on her existing plan.
The PM will meet German Chancellor Angela Merkel and French President Emmanuel Macron on Tuesday.
Mrs May's spokesman said she was also making calls to other European leaders from Downing Street on Monday afternoon.
She is due at an emergency summit in Brussels on Wednesday, where EU leaders will expect to hear fresh plans ahead of the UK's scheduled exit date - Friday at 23:00 BST.
Meanwhile, peers are continuing to examine a bill brought by senior Labour MP Yvette Cooper, which aims to force the PM to request a Brexit extension rather than leave the EU without a deal.
Despite communications over the weekend, there were no further talks with Labour scheduled for Monday.
However, Sir Keir - who is part of Labour's negotiating team - added: "I have no doubt things will develop today."
BBC political editor Laura Kuenssberg said the party was now "expecting [an] updated proposal" from the government, and more formal talks could take place this afternoon.
Foreign Secretary Jeremy Hunt said Mrs May was leaving "no stone unturned" to try and resolve Brexit, while Culture Secretary Jeremy Wright told BBC Radio 4's Today programme that all sides needed to be "prepared to compromise" to "fulfil the primary objective" of leaving the EU.
But shadow transport secretary Andy McDonald told BBC's Radio 4's Today programme that talks between the parties had "not been entirely productive".
Several Conservatives have also strongly criticised the move, with the former Foreign Secretary Boris Johnson using his column in Monday's Daily Telegraph to warn that Tory MPs would not allow Mrs May to "surrender" to Mr Corbyn.
The EU's chief Brexit negotiator, Michel Barnier, is in Dublin for talks with the Irish Taoiseach Leo Varadkar.
The pair are expected to discuss developments in London, as well as ongoing planning for a possible no-deal scenario.
On Sunday, Mrs May tweeted a video message, explaining her decision to negotiate with Labour, saying: "People didn't vote on party lines when it came to the Brexit referendum.
"And I think members of the public want to see their politicians working together more often."
If no compromise can be reached with Labour, Mrs May has committed to putting a series of Brexit options to the Commons and being bound by the result.
Sir Keir said the talks had been taking place "in good faith" and that "both sides... have approached this in the spirit of trying to find a way forward".
But he added: "At the moment we are waiting to see what the government is putting on the table as a proposal.
"All they have done so far is indicate various things but not to change the political declaration [the non-legally binding document setting out the UK's future relationship with the EU] so the ball is in the government's court.
"We need to see what they come back with and when we do we will take a collective position on that."
Rebecca Long-Bailey, who is also a member of Labour's negotiating team, described the mood as "positive and hopeful" - but she told the BBC's Andrew Marr show the government's proposals "have not been compliant with the definition of a customs union", which is her party's key demand.
That would allow tariff-free trade in goods with the EU but limit the UK from striking its own deals. Leaving the arrangement was a Conservative manifesto commitment.
However, Solicitor General Robert Buckland told BBC Radio 4's Westminster Hour that "something approximating a customs arrangement or customs union" was the most likely outcome of the talks.
"In this particular hung Parliament none of us can get perfection, we need to compromise," he added.
Ms Long-Bailey also suggested Labour could be prepared to cancel Brexit by revoking Article 50 - the legal mechanism through which Brexit is taking place - if the UK was heading towards a no-deal scenario on Friday.
Although 12 April remains, in law, the date the UK will leave the EU, Mrs May has already requested that be rescheduled until the end of June.
BBC political correspondent Vicki Young said if EU leaders did not think she had a credible plan to get Parliament behind a deal, they might refuse or insist on a much lengthier extension to the Brexit process.
This outcome is opposed by some Tory Brexiteers as it would mean the UK having to take part in European Parliamentary elections.
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PM Theresa May has struck a last-minute deal with the EU in a bid to move Brexit talks on to the next phase.
There will be no "hard border" with Ireland; and the rights of EU citizens in the UK and UK citizens in the EU will be protected.
The so-called "divorce bill" will amount to between £35bn and £39bn, Downing Street sources say.
The European Commission president said it was a "breakthrough" and he was confident EU leaders will approve it.
They are due to meet next Thursday for a European Council summit and need to give their backing to the deal if the next phase of negotiations are to begin.
Talks can then move onto a transition deal to cover a period of up to two years after Brexit, and the "framework for the future relationship" - preliminary discussions about a future trade deal, although the EU says a deal can only be finalised once the UK has left the EU.
A final withdrawal treaty and transition deal will have to be ratified by the EU nations and the UK Parliament, before the UK leaves in March 2019.
Northern Ireland's Democratic Unionist Party, whose opposition on Monday led to talks breaking down,  said there was still "more work to be done" on the border issue and how it votes on the final deal "will depend on its contents". Mrs May depends on the party's support to win key votes in Westminster.
The pound was trading at a six-month high against the euro as news broke of the draft agreement.
The UK government and the EU want to maintain the free flow of goods, without border checks that they fear could threaten a return to The Troubles, but the DUP does not want Northern Ireland to be treated differently to the rest of the UK after Brexit.
The joint EU-UK document says any future deal must protect "North-South co-operation" and hold to the UK's "guarantee of avoiding a hard border".
The agreement also says "no new regulatory barriers" will be allowed between Northern Ireland and the rest of the UK, and that Northern Ireland's businesses will continue to have "unfettered access" to the UK internal market - a passage thought to have been added to meet DUP concerns.
But it also sets out a fallback position if the UK fails to agree a trade deal. This could prove controversial because it says there will continue to be "full alignment" between the EU and Northern Ireland on some elements of cross-border trade, as set out in the Good Friday Agreement.
The DUP would have preferred this not to be in the agreement, says the BBC's Chris Morris, and there could be some hard negotiating to do further down the line.
Agreement has been reached on what happens to the three million EU citizens living in the UK and more than a million UK citizens in EU states after Brexit.
EU citizens currently in the UK would be allowed to continue living and working there - and those already in the country who do not yet have permanent residency would be able to acquire it after Brexit.
Freedom of movement could continue for two years after March 2019, although the UK says new arrivals will have to register.
The plan is that UK citizens in living in an EU country would get the same rights, although they would not retain them if they moved to another EU country.
For eight years after Brexit, UK courts will be able to refer cases involving EU nationals to the European Court of Justice for interpretation.
But the campaign group the 3million, which represents EU citizens in the UK, said there was "still no clarity around the registration criteria for these rights" and said of the eight years: "Our rights should not have an expiry date".
A figure is not mentioned in the text of the agreement but Downing Street sources says it will be between £35bn and £39bn.  It will be paid over four years and the precise figure is unlikely to be known for some time.
EU Brexit negotiator Michel Barnier said the EU had agreed to drop the cost of relocating UK-based EU agencies from the final divorce bill.
The prime minister said it would be "fair to the British taxpayer" and would mean the UK in future "will be able to invest more in our priorities at home, such as housing, schools and the NHS".
Technically a future trade deal cannot be signed while the UK remains a member of the EU but "preliminary and preparatory discussions" can begin.
But the EU's chief Brexit negotiator Michel Barnier has said the withdrawal treaty and transition deal need to be ready by October 2018 - in order that they can be ratified by March 2019, before the "real negotiation" begins on the future relationship.
Mr Barnier suggested on Friday that the only option for a future trade arrangement was a Canada-style deal, rather than a one based on Norway, which retains free movement and unrestricted access to the single market but pays into the EU budget.
The European Council wants the UK to remain a "member" of the EU's customs union and single market and to remain under the full jurisdiction of the European Court of Justice during the transition period, according to a leaked document.
The DUP, whose opposition on Monday led to talks breaking down, say there have been six "substantial changes" to the text.
Party leader Arlene Foster said they would mean there was "no red line down the Irish Sea" - meaning no customs barrier between Northern Ireland and the rest of the UK.
But BBC Northern Ireland economics editor John Campbell says there is a lot of hard negotiating to come and compromises to be made.
Another interpretation of the deal is that that it still leaves the door open for a special status for Northern Ireland, he adds.
What does Brexit deal mean for NI?
The prime minister made her decisions on Thursday night while the No 10 Downing Street Christmas party carried on.
It isn't celebration on Friday though for her government, but relief.
Theresa May's cabinet colleagues heaped praise on her, with Environment Secretary Michael Gove saying it was a "significant personal political achievement" for Mrs May while Foreign Secretary Boris Johnson tweeted: "Congratulations to PM for her determination in getting today's deal."
But Labour's Brexit spokesman Sir Keir Starmer said Mrs May should "seriously reflect on her approach to the negotiations so far".
He added: "Despite being two months later than originally planned, it is encouraging that the European Commission has recommended sufficient progress in the Brexit negotiations."
European press relieved at Brexit 'white smoke'
DUP Leader Arlene Foster said it meant that Northern Ireland would "not be separated constitutionally, politically, economically or regulatory from the rest of the United Kingdom" and "in all circumstances the United Kingdom will continue to ensure the same unfettered access for Northern Ireland's businesses to the whole of the UK internal market".
Scotland's First Minister Nicola Sturgeon tweeted: "Move to phase 2 of talks is good - but the devil is in the detail and things now get really tough."
Lib Dem leader Vince Cable, who backs a referendum on the final deal, said "it reduces the risk of a catastrophic no-deal Brexit" but questioned if it would last or be "torn apart by Theresa May's own MPs".
Former UKIP leader Nigel Farage told the BBC the estimated bill was "way more than we need to pay" and he was unhappy that the European Court of Justice would continue to have a role for up to eight years. "The whole thing is humiliating. We have collapsed at every level."

A plan that keeps the UK in the EU's single market may be backed by Labour leader Jeremy Corbyn, a Welsh MP has indicated.
After Prime Minister Theresa May's withdrawal agreement was defeated twice, MPs will look at other options.
Aberavon's Stephen Kinnock said "Common Market 2.0" puts "flesh on the bones of Labour's formal policy position".
The UK was due to leave the EU on 29 March but after MPs failed to agree on the terms, it has been pushed back.
Meanwhile, Conservative MPs David TC Davies and Robert Buckland have said brokering a deal this week must be a priority.
On Wednesday, MPs are expected to be allowed a vote on a range of Brexit options, in an attempt to achieve majority support for one way forward.
These include cancelling Brexit, holding another referendum - which is favoured by many Labour MPs, and leaving without a deal.
Mr Kinnock has for a long time made calls for the UK to remain as closely aligned to the EU as possible.
He told Sunday Politics Wales the "Common Market 2.0" plan would see a relationship similar to what Norway enjoys with the EU, with access to the single market.
But opponents have said this would leave the UK too closely aligned with the EU's rules such as making financial contributions and an element of freedom of movement.
Mr Kinnock said he had held very "constructive and productive" discussions with Jeremy Corbyn and Labour's Brexit spokesman Keir Starmer.
"I believe that this is a real opportunity to re-set our relationship with the European Union and to have one based on democratic consent," he said.
"We don't want to be part of that deeper, more political union but we want the Common Market, we want that strong market-based relationship."
Meanwhile, solicitor general Robert Buckland said people were "fed up of uncertainty".
"The Europeans are running out of patience. They've spent a lot of time on this," the Llanelli-born, Conservative South Swindon MP told BBC Radio Wales' Sunday Supplement programme.
"They had to wipe out a large part of their agenda. They wanted to talk about China and other issues to do with the internet.
"They've spent a lot of time on Brexit. They want this over."
He said he wanted the votes of MPs on options to be "tempered in the light of that reality".
"They (the EU) have made it clear - the way out is the withdrawal agreement," Mr Buckland added, in a plea for MPs to get behind Mrs May's twice-defeated deal.
And Monmouth MP David TC Davies said Theresa May had to do "whatever it takes" to get a Brexit deal agreed this week - even if it means standing down.

David Davis has warned against "putting politics above prosperity" in Britain's post-Brexit relationship with the EU.
In a speech in Berlin, the UK's Brexit Secretary outlined his hopes for a deal that "allows for the freest possible trade in goods and services".
He also said he thought it "incredibly unlikely" there would be no deal.
The EU says negotiations cannot move on to trade until questions about the UK "divorce bill", citizens' rights and Northern Ireland are resolved.
BBC political editor Laura Kuenssberg said Mr Davis's speech was delivered politely but implied "pretty significant frustrations on the UK side with the EU's attitude".
In a question and answer session following the speech, a German interviewer got a round of applause for suggesting the UK government looked to be "in chaos".
Mr Davis replied: "One of the issues in modern politics is that all governments have periods of turbulence.
"This is a period of turbulence, it will pass."
In his speech to an economic conference organised by the German newspaper Süddeutsche Zeitung, he said trade between Germany and the UK was worth 176bn euros a year or "more than a thousand euros to every man, woman and child in each of our countries".
He said the "close economic ties" with the EU "should continue, if not strengthen" after Brexit, and he warned: "Putting politics above prosperity is never a smart choice".
The UK was seeking a "deep and comprehensive free trade agreement" of a scope the EU had never seen before as well as "continued close co-operation in highly regulated areas such as transport, energy and data", he said.
Britain would use an independent trade policy to lead a "race to the top on quality and standards" rather than engage in a "race to the bottom" that would mean lower standards, he told the audience.
He said the EU and UK needed to "think creatively" about their post-Brexit relationship but stressed the need for a "time limited transition period" to implement the new arrangements.
"And that would mean access to the UK and European markets would continue on current terms. Keeping both the rights of a European Union member and the obligations of one, such as the role of the European Court of Justice.
"That also means staying in all the EU regulators and agencies during that limited period. Which would be about two years."
He added that tariff-free trade should be maintained and there must be an "effective dispute mechanism" for any disputes that may arise, that should be neither the UK courts, nor the European Court of Justice.
"It must be appropriate for both sides so that it can give business the confidence it needs that this partnership will endure."
In a question and answer session following his speech, Mr Davis laughed off a question about whether the UK would be prepared to pay 60bn euros to settle its financial obligations.
He said the UK's aim was that "nobody will have to pay more ... nobody will receive less" but would not give a figure that the UK would be prepared to pay.
Asked if he thought the Brexit negotiations would end in "no deal", he said: "I think that's incredibly unlikely."
While the UK government has not put a figure on the amount it is prepared to pay to settle the UK's obligations but it has been estimated at 20bn euros (about £18bn).
The Sun newspaper reported on Thursday that the prime minister was preparing to offer an additional £20bn to the EU to clear the way for talks about a transitional and future trade deal. Downing Street described that as "yet more speculation".
EU sources told the BBC last week that the UK had only two weeks left to make progress on the so-called withdrawal issues, including the amount the UK will pay as it leaves and Mr Davis's EU counterpart Michel Barnier said "time is pressing" to get agreement on the bill.

European Council President Donald Tusk has quoted lyrics from John Lennon's Imagine to suggest the door remains open to the UK staying in the EU.
Ahead of a Brussels summit he said of that prospect: "You may say I'm a dreamer, but I'm not the only one."
Theresa May, who has said the UK will honour the referendum vote to leave, was due to outline her plans for the issue of expats' rights to EU leaders.
Speaking at the summit she hailed the "constructive" start to Brexit talks.
The gathering of 28 EU member states' leaders comes the day after measures to enable Brexit dominated the Queen's Speech. Mrs May's Conservatives are still trying to secure the Commons support needed to pass their programme.
Mrs May told reporters as she arrived: "I'm going to be setting out some of the UK's plans particularly on how we propose to protect the rights of EU citizens and UK citizens as we leave.
"That's been an important issue. We've wanted it to be one of the early issues to be considered in the negotiations. That is now the case. That work is starting."
She also said she would be raising other important issues, including how European leaders could work together to stop the spread of extremism online and ensure there was no "safe space" online for terrorists.
Brexit negotiations began on Monday.
Speaking before the summit, Mr Tusk said: "It is a most difficult process, for which the EU is well prepared. You can hear different predictions coming from different people about the possible outcome of these negotiations - hard Brexit, soft Brexit or no deal.
"Some of my British friends have even asked me whether Brexit could be reversed and whether I could imagine an outcome where the UK stays part of the EU.
"I told them that, in fact, the European Union was built on dreams that seemed impossible to achieve. So, who knows. You may say I'm a dreamer, but I'm not the only one."
His comments were raised at a press conference in Brussels later with President of the European Commission, Jean Claude Juncker, who said: "In Europe, I never have illusions because I don't want to lose them."
But Mr Tusk said: "I still have dreams. Politics without dreams - it would be a nightmare."
"If you had my experience from my part of Europe you would know that miracles do happen and some of my political dreams have come true... but at the same time I am a realist, this is why first of all we should start our negotiations as effectively as possible and the final decision... this is a decision for Britain and UK citizens."
Earlier Chancellor Philip Hammond told BBC Radio 4's Today he wanted an early agreement on the principle of a "transitional" period to reassure business there would not be a "cliff edge" when the UK leaves the EU at the end of March 2019.
He also denied that a series of controversial Conservative manifesto commitments had been dumped in the wake of the disappointing election result.
He told Today that the manifesto was for a five-year period, but the Queen's Speech programme had been for the first two years, which are dominated by the process of Brexit.
Both the UK and the rest of the EU say they want to come to an arrangement to secure the status of about 3.2 million EU nationals living in the UK, and 900,000 Britons overseas, but nothing has been decided so far.
UK opposition parties have urged the government to make a unilateral guarantee to the EU migrants - but ministers have insisted a reciprocal deal is needed to ensure British expats are protected.
Mrs May will not be present when the leaders of the remaining 27 EU states hold a brief discussion about Brexit after her presentation. They are expected to consider the relocation of the two EU agencies governing medicine and banking which are currently based in London.
Of the 27 bills in the Queen's Speech, eight related to Brexit and its impact on immigration, trade and sectors such as fisheries and farming.
At the centre was the so-called Repeal Bill, which will copy over all EU laws into UK law, with Parliament then deciding which bits to retain.
With MPs voting on the speech next week, the Conservatives are hoping an  arrangement with Northern Ireland's Democratic Unionist Party will be in place to support their minority government.
But despite both sides saying they were confident of a deal being agreed, sources suggested to the BBC the DUP were "getting to the limits" of what they were requesting in return for supporting the Tories - with the chances of a plausible long-term deal, rather than a short-term bargain to get the Queen's Speech through, diminishing.
As well as clearing the Commons, Brexit legislation will also have to navigate the House of Lords, where the Tories also do not have a majority.
Another potential obstacle could emerge if the approval of the Scottish Parliament is needed for the Repeal Bill.
Speaking in the Commons after the Queen's Speech, Mrs May said there was a "possibility" the bill, which is needed to stop EU law applying in the UK, could require Holyrood's consent.
At the two-day summit, where the agenda is formally dominated by immigration, security and the economy, Mrs May will also brief her counterparts on the UK's commitment to a new £75m plan designed to stem the flow of illegal migrants from Africa to Europe.

Foreign Secretary Jeremy Hunt says "extra time" may be needed to finalise legislation for Brexit.
Mr Hunt said a possible delay in the UK's departure from the EU beyond the 29 March deadline depended on the progress made in the coming weeks.
The PM is seeking "alternative arrangements" to the backstop, but the EU says it will not renegotiate.
Parliament's February break has been cancelled, which No 10 said showed all steps were being taken to avoid delay.
The UK is due to leave the European Union at 23:00 on 29 March. The backstop is an "insurance" policy to stop the return of checks on goods and people along the Northern Ireland border.
Earlier this month, Commons Leader Andrea Leadsom said that the EU may be prepared to grant the UK a "couple of extra weeks" beyond the 29 March deadline to finalise preparations for Brexit.
And BBC political editor Laura Kuenssberg said there had been "growing chatter" about a potential delay and a potential extension to Article 50 - the mechanism by which the UK leaves the EU.
Labour leader Jeremy Corbyn said the government "has had two-and-a-half years to negotiate and has failed to do so".
But the prime minister's official spokesman said the government remained committed to leaving the EU on 29 March.
"The fact that recess won't be taking place shows you that we are taking all available steps to make sure that 29 March is our exit date," the spokesman said.
Downing Street was also discussing the possibility of Parliament sitting for extra hours in the run up to Brexit, the spokesman said.
Transport Secretary Chris Grayling said the government was "not talking about extensions" to Brexit at the moment, saying the focus should be "getting on with the job of completing the deal".
Mr Hunt told BBC Radio 4's Today programme: "It is true that if we ended up approving the deal in the days before the 29 March, then we might need some extra time to pass critical legislation.
"But if we are able to make progress sooner, then that might not be necessary. We can't know at this stage exactly which of those scenarios would happen."
Theresa May has been talking to a variety of MPs and EU leaders, including President of the European Council Donald Tusk and the Irish Taoiseach, Leo Varadkar, after MPs voted on Tuesday for her to make changes to the backstop.
Mr Hunt said it was a "challenging situation" and the government was "not ruling out" any  potential solutions to the Irish border issue.
He said the commitment to the Good Friday Agreement - which protects against the return of a hard border between Northern Ireland and the Republic of Ireland - would need to be demonstrated.
The EU's concerns that the UK could "access the single market by the back door" would also need to be alleviated, he said.
"If we can overcome those two issues, which I think we can, then we will be able to have substantive discussions," he said.
The backstop was one of the main reasons Mrs May's Brexit deal was voted down in Parliament by a record margin earlier in January because critics say a different status for Northern Ireland could threaten the existence of the UK and fear that the backstop could become permanent.
Alternatives to the backstop that the prime minister has said she wants to discuss with EU leaders include:
She also wants to discuss a time limit on the backstop and a "unilateral exit" mechanism - both options ruled out by the EU in the past.
The EU's chief negotiator, Michel Barnier said on Wednesday that the Irish backstop was "part and parcel" of the UK's Brexit deal and would not be renegotiated.
Several Conservative MPs have been spotted going to meetings in Downing Street, including former Brexit minister Steve Baker, Iain Duncan Smith, Mrs May's close ally Damian Green and Nicky Morgan.
Ms Morgan, a former education secretary, said she was there to discuss a plan known as the "Malthouse Compromise".
Engineered by both Leavers and Remainers, the proposal includes extending the transition period for a year and protecting EU citizens' rights, instead of using the backstop.
Union officials have also been meeting with government officials in the Cabinet Office to discuss Mrs May's Brexit plan.
A Trades Union Congress spokesman said the prime minister's deal came "nowhere close" to offering the safeguards desired for working people.
"The strongest possible protection for workers' rights would come from sticking by single market and customs union rules," he said.
When asked about a Times article that said Mrs May was preparing to entice Labour MPs to vote for her deal with money for constituencies, Labour MP John Mann said a group of 10 met the prime minister two weeks ago.
Mr Mann, who was also spotted in Downing Street on Thursday, told the BBC the group asked for "a significant amount of money" for poorer areas, "so that we can actually move forward as we leave the EU".
But he said he had voted for the deal already, "so I can't be bribed".
"There's no expectation, this isn't transactional politics. We're asking for money for areas that have not had their fair share in the past," he said.
Meanwhile, Mrs Leadsom told MPs that "in light of the significant decisions taken by the House this week" she was giving the House notice that "there are currently no plans to bring forward a motion to agree dates for the February recess".
Parliament had been due to rise for recess on Thursday, 14 February and return on Monday, 25 February.
Mrs Leadsom said she realised it was short notice, but said their constituents "would expect that the House is able to continue to make progress at this important time".
Labour leader Jeremy Corbyn accused the government of running down the clock on Brexit.
He said: "We delayed the parliamentary vote from 11 December until January - and then lost by the biggest majority ever against a government.
"Now we're going back to Brussels but we are very unclear about what we're going back to Brussels to do and when I asked the prime minister about this yesterday, she was incredibly vague.
"It is possible that there will have to be an extension in order to get an agreement because we cannot leave the EU on March 29 without an agreement. Crashing out would mean problems of transport, problems of medicine supply, problems of supply to the food processing industry that does just in time deliveries - and that simply is not acceptable.
"This government has had two-and-a-half years to negotiate and has failed to do so."

Labour has said leaked government papers "confirm its worst fears" about plans to dilute workers' rights after Brexit.
The documents, revealed by the Financial Times, say that the drafting of commitments on workers' rights and the environment in the Brexit deal "leaves room for interpretation".
Labour said it is a "blueprint" for ending "vital rights and protections".
But Business Minister Kwesi Kwarteng said the claims are "way exaggerated".
The leaked paper suggests that the government believes there is considerable scope to diverge from the EU on employment rights and other regulations after Brexit, despite its pledge to maintain a "level playing field" in Boris Johnson's latest deal.
In Mr Johnson's Brexit deal, references to a level playing field - the idea that the UK and EU countries keep their rules and standards close to prevent one trying to gain a competitive advantage - were removed from the legally binding withdrawal agreement.
Instead, they were put into the non-binding "political declaration", which describes the potential future relationship between the UK and EU.
According to the FT, the leaked document says the UK's and EU's interpretation of the "level playing field" pledge will be "very different", and the text represents a "much more open starting point" for negotiations over a future trade deal.
Purportedly drafted by the Brexit department, the paper appears to contradict promises by the prime minister on Wednesday that the UK is committed to the "highest possible standards" for the environment and rights at work.
It comes as EU leaders consider their decision on a new deadline for Brexit, having agreed to an extension in principle after the UK government admitted it could not meet its 31 October deadline.
The document will fuel fears among some in the EU that Boris Johnson is planning to shape Britain into a Singapore-style economy, with low taxes and light regulation, which could compete against Europe by potentially downgrading rights.
Suggestions that workers' rights could be diluted will also raise concerns among Labour MPs, 19 of whom voted for the Withdrawal Agreement Bill to progress in the House of Commons.
Labour shadow Brexit minister Jenny Chapman said the documents "confirm our worst fears".
She said: "Boris Johnson's Brexit is a blueprint for a deregulated economy, which will see vital rights and protections torn up."
The Brexit department said it did not recognise the document, however.
And Business Minister Kwesi Kwarteng told the BBC the claims were "completely mad" after the government had worked to win the support of Labour MPs.
"It wouldn't make any sense at all to dilute workers' rights in building that coalition to land the bill," he said.
"We have said we will be better than our word. We have said our ambition on securing workers' rights will be stronger than the provision of the bill."
Environmental groups have also raised concerns after the document was leaked, calling on ministers to introduce legal guarantees on current standards in the Environment Bill, which is due to be debated for the first time in the Commons on Monday.
Benjamin Halfpenny from Greener UK, a coalition of groups including the RSPB, Friends of the Earth and the National Trust, said: "The government has had plenty of opportunities to put a commitment to existing standards into law, but has thus far not done so.
"Such a commitment would not prevent future governments from going further on things like water quality and chemical safety, just stop them going backwards."
A Brexit department spokesman said the government "has no intention of lowering the standards of workers' rights or environmental protection after we leave the EU".
He said the UK already exceeds the minimum standards in areas such as maternity leave, shared parental leave and greenhouse gas emissions targets.

Labour's deputy leader Tom Watson has described another Brexit referendum as "the least worst option" and urged his party to throw its weight behind one.
Speaking to the BBC, he said Labour should then fight for Remain, even though "we might lose some votes".
Jeremy Corbyn has resisted calls to fully endorse another public vote, only calling for it in some circumstances.
But Mr Watson said Labour would pay "a very high electoral price" if it did not have "a clear position" on Brexit.
The nuanced position was blamed for Labour's performance at the European elections - it came third behind The Brexit Party and the Liberal Democrats, with its share of the vote falling to 14%.
Afterwards, several senior figures criticised a lack of clarity on Brexit, and last week, MPs expressed their frustration at a heated meeting of the Parliamentary Labour Party.
The PLP is still split, though, with some MPs in Leave-supporting areas warning against backing a further public vote.
The shadow cabinet was due to meet on Monday to discuss Brexit, but the meeting has been postponed.
Mr Watson - who has repeatedly put pressure on Mr Corbyn to back a further referendum - told the BBC's political editor Laura Kuenssberg he believed it was now the only choice available.
Theresa May's Brexit deal with the EU has been rejected by Parliament three times and the UK currently has until 31 October to come up with another way to leave.
"Sometimes in politics your choices are the least worst option," Mr Watson said. "It is my honestly held view that Parliament will not be able to get a deal on Brexit and therefore the only choice, reluctantly, is to ask the people to take another look at it."
When asked if he would leave the Labour Party if things did not change, he replied, "I'm never going to leave the Labour Party," but added "sometimes I wonder whether the Labour Party is leaving me."
Earlier, in a speech to the Centre for European Reform, the deputy leader said Labour must be honest about the EU's strengths.
"Pro-European is who we are and who we have always been. Our members are Remain. Our values are Remain. Our hearts are Remain."
He told the BBC Labour "might lost some votes if we change position", but added: "I think it's incumbent on us to give an honest account of ourselves and make the case for why we've changed our position."
Mr Watson is calling for a one-off meeting or ballot of members to be held to vote on a shift in policy - warning Labour could not afford to wait until its party conference in late September.
But as he gave his speech, Labour chairman Ian Lavery - who is against another referendum - tweeted that "ignoring Leave voters" was not a sensible move.
Labour MP John Mann warned adopting an overtly Remain position would lead to Labour losing the next general election "by a significant amount".
He said if Labour "turned its back" on voters in the North who voted Leave, "then Tom Watson won't be deputy, Jeremy Corbyn won't be prime minister."
Labour MP Kerry McCarthy said she would commend Mr Watson for "speaking out", but shadow ministers needed to "meet urgently for a proper discussion on Brexit".
"We need to be clear where Labour stands, and if [the] shadow cabinet can't agree, put it to the members," Ms McCarthy posted on Twitter.
Mr Watson has received support from a number of colleagues, including Jess Phillips and Anna Turley.
Another MP, Siobhain McDonagh, tweeted: "I have had my differences with Tom Watson over the years but this video is brilliant and his argument is bang on! So many Labour members will be cheering him on!"
Laura Kuenssberg says plenty of Labour MPs are worried because they represent constituencies with Leave voters, but there is no question the balance in the party is on the other side.
"There are plenty of senior people - including those absolutely loyal to Jeremy Corbyn - who think it is time for the leadership to make a clearer statement arguing for another referendum and for Britain to stay in EU," she says.
"Some of those think it is vital to do before the summer and they predict we may end up with an election in the autumn with the Tories arguing for Leave and Labour arguing for Remain."
However, Mr Watson said all strands of opinion within the party are entitled to be heard.
He also argued that the "core" EU values of internationalism, solidarity and freedom are also the values of Labour.
"Some people have begun to equate support for Europe with class identity - I don't think that's right or helpful," he said.
"The majority of Labour people are supportive of Europe and that support is not dictated by social class."

Negotiators from the UK and EU are having what has been described as "intense technical discussions" in an attempt to agree a new Brexit deal.
About a dozen British officials, including the UK's EU adviser David Frost, are taking part in the talks at the EU Commission in Brussels.
The meetings are expected to continue through the weekend.
But European Council President Donald Tusk has suggested there is only the slightest chance of an agreement.
The UK is due to leave the EU at 23:00 GMT on 31 October and a European leaders' summit next Thursday and Friday is seen as the last chance to agree a deal before that deadline.
Prime Minister Boris Johnson's revised proposals - designed to avoid concerns about hard border on the island of Ireland after Brexit - were criticised by EU leaders at the start of last week.
However, on Thursday, Mr Johnson and the Irish prime minister Leo Varadkar held talks and said they could "see a pathway to a possible deal".
BBC Europe reporter Gavin Lee said there is no scheduled timetable for the discussions in Brussels and neither the UK or EU are offering any detail yet on the apparent common ground that has been found on the Irish border.
Our correspondent said the first public announcement on the talks may come on Monday, after the EU's 27 ambassadors have been updated on the progress so far.
Meanwhile, shadow Brexit secretary Sir Keir Starmer says Labour would take action through the courts if Mr Johnson tries to push through a no-deal Brexit.
Addressing the Co-operative Party conference in Glasgow, Sir Keir said if the PM did not secure a deal at the EU summit on 17 and 18 October, he must comply with the so-called Benn Act passed by MPs in September, which requires him to seek a further delay.
"If he doesn't, we'll enforce the law - in the courts and in Parliament. Whatever it takes, we will prevent a no-deal Brexit," he said.
This weekend's talks in Brussels follow a meeting on Friday between Brexit Secretary Steve Barclay and EU chief negotiator Michel Barnier, described by both sides as "constructive".
In a statement issued later, the European Commission said: "The EU and the UK have agreed to intensify discussions over the coming days."
Speaking on BBC Radio 4's Today programme, Culture Secretary Nicky Morgan reiterated that "lots of details" needed to be worked out between both parties but said the "mood music" on negotiations "seems positive".
She added that "speculation doesn't really help" and politicians needed to "stand back and give those negotiations and discussions the best chance of succeeding".
On Friday, Mr Tusk said he had received "promising signals" from the Irish PM, before adding: "Of course there is no guarantee of success and time is practically up, but even the slightest chance must be used".
Mr Johnson also acknowledged there was not "a done deal", saying: "The best thing we can do now is let our negotiators get on with it."
Support from Democratic Unionist Party MPs could be crucial to get a deal through Parliament.
But DUP leader Arlene Foster said: "Anything that traps Northern Ireland in the EU... will not have our support."
Brexiteer Sir John Redwood believes Mr Johnson should "table a free trade agreement" which would "unlock" most of the issues around borders and immigration.
He added: "I think the border issue is greatly exaggerated, because it is in the interest of the European Union and Ireland to exaggerate it."
Ms Morgan was asked on the Today programme about reports of Downing Street briefings that the Tories could contest a general election on a no-deal Brexit ticket, if an agreement cannot be reached.
The Loughborough MP - who voted Remain - did not say whether she would contest an election on such a ticket, but said reports that Mr Johnson is preparing to fight a general election on a no deal platform are "wide of the mark".
Monday 14 October - The Commons is due to return, and the government will use the Queen's Speech to set out its legislative agenda. The speech will then be debated by MPs throughout the week.
Thursday 17 October - Crucial two-day summit of EU leaders begins in Brussels. This is the last such meeting currently scheduled before the Brexit deadline.
Saturday 19 October - Special sitting of Parliament and the date by which the PM must ask the EU for another delay to Brexit under the Benn Act, if no Brexit deal has been approved by Parliament and they have not agreed to the UK leaving with no-deal.
Thursday 31 October - Date by which the UK is due to leave the EU, with or without a withdrawal agreement.

The UK and EU say key issues remain unresolved following unscheduled Brexit talks in Brussels.
Brexit Secretary Dominic Raab and EU chief negotiator Michel Barnier met for more than an hour ahead of a crunch EU leaders' summit this week.
Mr Barnier tweeted that issues, such as how to avoid a hard border with Ireland, were "still open".
A UK government spokesman said UK and EU negotiators "have made real progress in a number of key areas".
"However there remain a number of unresolved issues relating to the backstop," he added.
BBC political editor Laura Kuenssberg said talks had "made progress" in the last few days - and dismissed reports of a row between Mr Raab and Mr Barnier - but added it was "clear the two sides are stuck" on how the Irish backstop might work.
No further talks are planned before Mr Barnier and Theresa May's summit on Wednesday, she added.
The meeting comes as domestic political pressure on Mrs May increases amid threats of potential cabinet resignations.
In a letter to the prime minister, Scottish Secretary David Mundell and Scots Tory leader Ruth Davidson said they would not accept Northern Ireland being treated differently from the rest of the UK in any Brexit deal.
It follows reports that other top ministers have been considering their positions over the weekend ahead of a meeting of the cabinet on Tuesday at which ministers could be asked to give their consent to any agreement.
By BBC political editor Laura Kuenssberg
While there may have been a sense in Brussels that Mrs May was moving towards them, if anything the politics at home have become more fraught.
Thursday's cabinet meeting ramped up concerns and gave Brexiteers another excuse to rattle their sabres.
The DUP continues its warnings that it'd sink the administration rather than see the deal it fears done. Several cabinet ministers are thinking about whether they can go on.
And, more to the point, different groups of Tory MPs with gripes about other policies are scenting opportunity as the government is so vulnerable.
Any move for the PM has become both harder, and more urgent.
Her party won't accept a proposal to keep the UK essentially in the customs union. Parliament is likely to block no deal. The EU won't accept her Chequers plan.
Even loyal ministers are deeply worried - "She is like a chess player who only has the king left - all she can do is move one square at a time until she is check-mated."
The Raab-Barnier meeting came amid conflicting signals as to whether the two sides were nearing a deal on the terms of the UK's exit next March.
Diplomats from the remaining 27 EU member states were summoned for an update on the process at 17.30 BST, prompting feverish speculation that a deal had been done.
The BBC's Brussels reporter Adam Fleming said that while Mr Raab's visit had an air of drama, it was standard practice in the talks for civil servants to hand over to politicians at key points like this.
Rather than a "victory lap" by Mr Raab, he said the UK's statement that "face-to-face talks were necessary to resolve several big issues" should be taken at face value, and Northern Ireland remained a "sticking point".
The issue of the border between Northern Ireland and the Republic of Ireland, which will become the UK's border with the EU, is one of the last remaining obstacles to achieving a divorce deal with Brussels.
Wrangling is continuing over the nature of a "backstop" to keep the border open if a wider UK-EU trade arrangement cannot resolve it.
The EU's version, which would see just Northern Ireland remain aligned with Brussels' rules, has been called unacceptable by Mrs May and her Democratic Unionist allies.
And many Conservative MPs are unhappy with the UK government's proposed alternative, which would see the UK temporarily remain in a customs union until the Irish border question is resolved, either through technological solutions or as part of a wider trade agreement.
Brexiteers fear this will leave the UK in indefinite limbo, bound by the EU's rules and limited in the trade deals it can negotiate with other countries.
Writing in the Sunday Times, former Brexit Secretary David Davis urged ministers to "exert their collective authority" and reject the plans at a cabinet meeting on Tuesday.
But Foreign Secretary Jeremy Hunt, who has been hosting other European foreign ministers at his Chevening residence, said such calls were "wrong" when "last-minute" talks were going on and Mrs May was "battling for Britain".
"The reason that's wrong is there is no-one who is going to be able to negotiate the right deal for Britain better than Theresa May. This is the time to stand rock solid behind Theresa May."
In their letter to the PM, Mr Mundell and Ms Davidson indicated they would not tolerate a situation in which Northern Ireland remained in the customs union and single market, while the rest of the UK was outside it.
They said the integrity of the UK "remains the single most important issue for us" and cannot be undermined by any withdrawal agreement with the EU.
A source close to Ms Davidson said the issue was a "red line" for her, while a source close to Mr Mundell told the BBC: "If you find yourself not agreeing with government policy" resigning would be the "logical outcome".
Health Secretary Matt Hancock, in an interview with the BBC's Andrew Marr show, insisted there were "different ways" to ensure any customs commitments were "credibly time-limited".
And Scottish First Minister and SNP leader Nicola Sturgeon, who wants Scotland to remain in the EU, has questioned whether Mr Mundell and Ms Davidson had "the gumption" to resign.

Donald Tusk has issued a "last call" to the UK to "lay the cards on the table" if a Brexit deal is to be done in time.
The European Council president said the "most difficult" issues were unresolved and "quick progress" was needed if agreement was to be reached by October.
Talks continue over the terms of the UK's withdrawal from the EU in March next year. What happens to the Irish border remains a sticking point.
The UK says both sides want to see a "faster pace" in talks.
But Prime Minister Theresa May has been unable to say much new at this summit - the last one before October - because she has yet to get her cabinet to agree on a blueprint for the UK's future relationship with the EU.
They are due to meet at Chequers next Friday, in what has been billed as a make-or-break meeting. Mrs May has said the UK will then publish a White Paper setting out "in more detail what strong partnership the United Kingdom wants to see with the European Union in the future".
Chancellor Angela Merkel said Mrs May would "come to Germany and we will have a longer debate on this", once the proposals were published.
At the close of the summit, Mr Tusk told reporters there was a "great deal of work ahead" on Brexit and the "most difficult tasks are still unresolved".
"Quick progress" was needed if a deal was to be reached at the next summit.
"This is the last call to lay the cards on the table," he said.
By the BBC's political editor Laura Kuenssberg
European leaders can repeat the same message, louder and louder.
But this EU summit's instructions to Theresa May may as well have been shouted into an empty cupboard.
Because they know what she knows - that the past 24 hours of Brexit conversations are not nearly as important as the next seven days of discussions at home between Number 10 and the rest of the government.
And after more than two years, this time next week ministers should be nearing the conclusion of their country retreat at Chequers.
It's there that the prime minister hopes to find resolution in her team on a more detailed offer to the rest of the EU - easing, if not removing, all the contradictions in the Tories' positions.
He was one of a string of EU chiefs demanding more clarity from the UK prime minister, who left the summit before the 27 other EU leaders discussed Brexit together on Friday.
European Commission President Jean-Claude Juncker said the British had to "make clear their position" adding: "We cannot go on to live with a split cabinet. They have to say what they want and we will respond to that."
EU chief Brexit negotiator Michel Barnier warned: "The time is very short" and that while progress had been made, "huge and serious divergence remains, in particular on Ireland and Northern Ireland".
He also said he hoped to see "workable and realistic" proposals from the UK on what the future relationship between the UK and EU should look like.
He said he was "ready to invite the UK delegation to come back to Brussels next Monday" to continue working on a deal.
BBC political editor Laura Kuenssberg said she understood that UK officials had already informed the EU Commission they would not hold talks on Monday and the "mini row over diaries" revealed "how tetchy things are".
European leaders at the summit welcomed progress on the legal text of the withdrawal agreement but noted that "important aspects still need to be agreed" including the territorial application of the deal "notably as regards Gibraltar".  Talks between Spain and the UK over Gibraltar, including access to its airport and the exchange of tax information, continue.
They also expressed concern that "no substantial progress has yet been achieved on agreeing a backstop solution for Ireland/Northern Ireland", if a deal on customs arrangements is not agreed by December 2020. when the transition period is due to end.
And they called on member states and EU institutions "to step up their work on preparedness at all levels and for all outcomes" - the European Commission president has said the EU must prepare for the possibility that no Brexit deal will be reached.
Mrs May's own cabinet is divided over what the UK's customs arrangements after December 2020 should look like, when the transition period agreed with the EU is due to end.
And there are disagreements over the future movement of goods and people across the border between Northern Ireland and the Republic of Ireland.
But asked if he believed Mrs May could resolve the differences, Mr Juncker told the BBC he knew the prime minister and: "yes ... she will".
On Thursday, Mrs May said a strong future partnership with the EU was in everyone's interests.
"I think both sides are keen to continue that work at a faster pace than we have done up till now and certainly we would welcome that," she said.
She added that the UK would publish a White Paper setting out "in more detail [the] strong partnership the United Kingdom wants to see with the European Union in the future".
But she urged fellow EU leaders to tell their negotiators the UK should be allowed to continue to take part in schemes like the Prum mechanism for sharing DNA profiles, the Second Generation Schengen Information System - a database of "real time" alerts about certain individuals - and the European Criminal Records Information System.
Without UK participation in such schemes, she suggested their collective ability to fight terrorism would be reduced.
Mrs May's Europe adviser Olly Robbins and Brexit Secretary David Davis were due to appear in front of the UK's Brexit select committee next week but it is understood that the appearance has been delayed until after the publication of the White Paper.
Former Brexit minister Lord Bridges, who backed Remain in the EU referendum, told the Evening Standard there was a risk negotiations could become a "rout", if the cabinet could not compromise, first with each other, then with Europe.
"If nothing changes, there's a danger the UK will have to agree to a withdrawal treaty full of meaningless waffle on our future relationship with the EU," warned Lord Bridges.
"With so little leverage in the next phase, the negotiations would become a rout. Worse, uncertainty will drag on, damaging our economy."

Theresa May says she has secured "legally binding" changes to her Brexit deal, a day ahead of MPs voting on it.
But European Commission President Jean-Claude Juncker warned if the deal was voted down there was "no third chance".
They spoke at a joint press conference in Strasbourg after a late meeting.
Labour leader Jeremy Corbyn said the prime minister's negotiations had "failed" and the announcements did not contain "anything approaching the changes" she had promised Parliament.
Cabinet Office Minister David Lidington announced the changes to the Commons shortly before the press conference, saying they would mean the EU "cannot try to trap the UK in the [Irish] backstop indefinitely".
Mrs May confirmed she would be opening the debate on Tuesday ahead of a so-called "meaningful vote" on her deal, which must be agreed by Parliament to come into force.
Last time her deal was put to Parliament in January, she suffered an historic loss as it was voted down by a margin of 230.
The PM also said her attorney general, Geoffrey Cox, would publish his legal advice on the changes to the deal before the vote.
By BBC political editor Laura Kuenssberg
Monday morning government blues have been replaced by Tuesday morning nervous hopes.
The government does not suddenly expect its Brexit deal to be ushered through at speed, cheered on by well-wishers.
It does, however, believe that Monday night's double act in Strasbourg by Theresa May and Jean Claude Juncker puts it, to quote one cabinet minister, "back in the races".
The extra assurances wrought from weeks of talks with the EU will move some of the prime minister's objectors from the "no" column to the "yes".
Read Laura's blog here.
Mrs May flew out to the European Parliament late on Monday with her Brexit Secretary Steve Barclay for last-ditch talks ahead of the vote.
In the discussions with Mr Juncker and the EU's chief Brexit negotiator Michel Barnier, two documents were agreed by all parties, which Mr Lidington said would "strengthen and improve" both the withdrawal agreement from the EU and the political declaration on the future relationship.
The first is a "joint legally binding instrument" on the withdrawal agreement.
Mrs May said it could be used to start a "formal dispute" against the EU if it tried to keep the UK tied into the backstop - the safety net designed to maintain an open border on the island of Ireland - indefinitely.
The backstop has been criticised by some who believe it will keep the UK tied to the EU indefinitely, but the bloc has said "if used [it] will apply temporarily".
The second is a "joint statement" adding to the political declaration - the statement in the deal about the UK and EU's future relationship - to commit to replacing the backstop with alternative arrangements by December 2020.
Another document will also be put forward by the government, known as a "unilateral declaration".
The PM said this would outline the UK's position that there was nothing to prevent it from leaving the backstop arrangement if discussions on a future relationship with the EU break down and there is no prospect on an agreement.
Mrs May said: "MPs were clear that legal changes were needed to the backstop. Today we have secured legal changes.
"Now is the time to come together to back this improved Brexit deal and deliver on the instruction of the British people."
Mr Juncker also warned MPs that they would be putting everything at risk if they voted down the deal.
"In politics sometimes you get a second chance," he said.
"It is what we do with that second chance that counts. There will be no third chance."
He added: "Let us speak crystal clear about the choice - it is this deal or Brexit might not happen at all."
Labour leader Mr Corbyn urged MPs to vote against the deal when it returns to the Commons on Tuesday.
"Since her Brexit deal was so overwhelmingly rejected, the prime minister has recklessly run down the clock, failed to effectively negotiate with the EU and refused to find common ground for a deal Parliament could support," he added.
The Conservatives' partner in Parliament, the DUP, have been outspoken critics of the deal - especially the backstop.
After the announcement, a spokesman said: "These publications need careful analysis. We will be taking appropriate advice, scrutinising the text line by line and forming our own judgement."

Did anything change? Not that much.
But for Downing Street, this has not been a pointless stop-off in the almost never-ending Brexit adventure.
Because, while there hasn't been a breakthrough, the EU has agreed to more talks, which at least opens up the possibility of discussing the changes to the troubled backstop that has caused such political difficulty.
It might not sound like much, but "we can talk", is at least a different message to "this is over" .
In the perception war, which is, of course, part of this whole battle, Theresa May didn't leave Brussels with nothing.
And in these torrid times, given the last summit before Christmas, (remember, nebulous?) going home with a process, if not a promise, counts for something.
That does not, for the avoidance of doubt, remotely make the prime minister's next steps easy.
The EU's suggestion that a compromise with Labour might sound tempting and practical. It's also a step forward for some Tory MPs who are pushing for a softer compromise.
But as we've discussed here so many times, moving to a softer Brexit could result in the downfall of the government, it could be that simple.
David Lidington and Keir Starmer might sit down to talk within days, but there are evidently costs for both of the main Westminster parties if they work together to get this deal through.
On the EU side, where so many governments are coalitions, the idea of cross-party working has an inevitable logic. But at this stage, straightforwardly, that is not the government's chosen way out.
As things stand, the Opposition wants to find compromise and the European Union wants to talk.
Sounds good? It doesn't work like that.
Because the interpretation of the political reality in most of the government, is that Theresa May won't shift to meet Labour, not yet.
And Brussels won't move yet to meet her.
And as the clock runs down, the pressure on the prime minister goes up and up with no obvious way out.
But making a big switch simply carries too many political risks, at this stage.
Just keeping going doesn't sound like a cunning political strategy but perhaps, right now, it's the only and best plan.

The chancellor has warned manufacturers that "there will not be alignment" with the EU after Brexit and insists firms must "adjust" to new regulations.
Speaking to the Financial Times, Sajid Javid admitted not all businesses would benefit from Brexit.
The Food and Drink Federation said it sounded like the "death knell" for frictionless trade with the EU and was likely to cause food prices to rise.
Mr Javid declined to specify which EU rules he wanted to drop.
The automotive, food and drink and pharmaceutical industries all warned the government last year that moving away from key EU rules would be damaging.
But Mr Javid told the paper: "There will be an impact on business one way or the other, some will benefit, some won't."
He said Japan's car industry was an example of a manufacturing sector which found success without following EU rules.
Asked how differing regulations between the UK and EU may impact industries such as automotive and pharmaceuticals, he said: "We're also talking about companies that have known since 2016 that we are leaving the EU.
"Admittedly, they didn't know the exact terms."
Tim Rycroft, chief operating officer of the Food and Drink Federation, told BBC Radio 4's Today programme that "it sounds awfully like the death knell for the concept of frictionless trade with the EU".
He said it probably meant that food prices would rise when the transition period finishes at the end of this year.
Mr Rycroft acknowledged that some other industries might benefit from UK-specific trade rules. But he said: "We also have to make sure the government clearly understands what the consequences will be for industries like ours if they go ahead and change our trading terms."
The Confederation of British Industry (CBI) said it welcomed the chancellor's "ambitious" vision but said government should not feel it has an "obligation" to depart from EU rules.
Carolyn Fairbairn, CBI director-general, said for many companies, "particularly in some of the most deprived regions of the UK", keeping the same rules would support jobs and maintain competitiveness.
The Society of Motor Manufacturers and Traders said the automotive industry in the UK and EU was "uniquely integrated" and its priority was to avoid "expensive tariffs and other 'behind the border' barriers".
It said it was vital to have "early sight" of the government's plans so companies could evaluate their impact.
The government has not yet agreed a future trading relationship with the EU - it plans to do so in the 11-month transition period which begins after the UK leaves the bloc on 31 January.
During the transition period the UK will continue to follow EU rules and contribute to its budget.
The chancellor also said he wanted to double the UK's annual economic growth to between 2.7 and 2.8%.
However, the outgoing governor of the Bank of England, Mark Carney, told the Financial Times last week he thought the UK's trend growth rate was much lower, at between 1 and 1.5%.
Mr Javid said the extra growth would come from spending on skills and infrastructure in the Midlands and the north of England - even if they did not offer as much "bang for the buck" as projects in other parts of the country.
Historically low interest rates, which allow the government to borrow money relatively cheaply, were "almost a signal to me from the market - from investors - that here's the cash, use it to do something productive", Mr Javid said.
He pledged to rewrite Treasury investment rules, which have tended to favour government investment in places with high economic growth and high productivity.
Mr Javid said the rules had helped to "entrench" inequality and insisted weaker parts of the country would have first call on the new money.
In November, the Bank of England said a weaker global economy and its new assumptions about Brexit would knock 1% off UK growth over the next three years compared with its previous August forecast.

A government source has told the BBC there will be "no deal tonight", as officials continue to work on the technical details in Brussels.
The UK and EU had been hoping to sign off a revised Brexit deal before Thursday's crunch EU council meeting.
Boris Johnson has been trying to get Tory Brexiteers and the DUP to back his revised plan for Northern Ireland.
The new draft Brexit deal has a mechanism enabling Northern Ireland to approve or reject the border plans.
This would give the Stormont Assembly the chance to vote on Brexit arrangements four years after the transition period ends in 2020.
The EU believes this replaces the controversial Northern Ireland backstop with arrangements that are sustainable over time and are democratically supported, as requested by the UK.
The backstop was designed to avoid a hard border on the island of Ireland after Brexit and involved the UK potentially retaining a very close relationship with the EU - staying in the customs union - for an indefinite period.
The legal text of the draft still has to be approved by the British government.
BBC political editor Laura Kuenssberg said she understood the issues between the UK, EU and Ireland were "pretty much sorted", but that DUP sources were warning there were still gaps between proposals and what the party could support.
The Democratic Unionist Party has propped up the Conservative government since the 2017 general election and their support could be vital if Parliament is to approve any agreement Mr Johnson secures.
Earlier, the PM likened the Brexit talks to climbing Everest, saying the summit was "not far" but still surrounded by "cloud".
He will travel to Brussels to attend the EU Council summit on Thursday.
The UK is due to leave the EU at 23:00 GMT on 31 October and Mr Johnson has repeatedly insisted this will happen, regardless of whether there is a deal or not.
The EU's chief negotiator Michel Barnier has, meanwhile, been briefing EU ambassadors, ahead of Thursday's summit - the meeting was originally due to take place at lunch time but was put back twice.
Asked afterwards, whether there was a deal, Mr Barnier said: "We are working, we are working."
The issue of the Irish border - and how to handle the flow of goods and people across it once it becomes the border between the UK and the EU after Brexit - has long been a sticking point in the negotiations.
The border is also a matter of great political, security and diplomatic sensitivity in Ireland.
Mr Johnson's proposals for a new Brexit deal hinge on getting rid of the backstop - the solution to border issues agreed by Theresa May which proved unpalatable to many MPs.
However, his plans would see Northern Ireland treated differently from the rest of the UK - something the DUP, among others, has great concerns about.
The DUP has, in particular, been demanding assurances around the so-called consent mechanism - the idea the prime minister came up with to give communities in Northern Ireland a regular say over whatever comes into effect.
A source told Newsnight's political editor Nick Watt the thinking in Number 10 was that "the DUP never want to own a solution - at some point you have to call their bluff. You just have to hope they will sulkily acquiesce."
The party's leader, Arlene Foster, held talks in Downing Street on Tuesday night and Wednesday morning.
As well as the DUP, Mr Johnson is also trying to secure support from Tory Brexiteers, most of whom are part of the European Research Group.
Chairman Steve Baker told reporters after a meeting in Downing Street on Wednesday evening his group "hope [to] be with the prime minister, but there are thousands of people out there who are counting on us not to let them down and we are not going to".
"We are just really wishing the prime minister well and hoping he has total success. We know there will be compromises, but we will be looking at this deal in minute detail with a view to supporting it, but until we see that text, we can't say."
As Wednesday draws to a close, a deal is still, DBP - difficult but possible, in case you haven't caught the lingo by now.
I hear from both sides of the Channel that the issues between the UK, Ireland and the EU are pretty much ironed out.
A schedule is in place for EU leaders to be able to sign off a deal tomorrow, discussing it as the first item on the agenda at the summit if the ink is dry.
The government has in place its plan to ask MPs to approve the hypothetical deal in Parliament on Saturday.
Despite all the obstacles, all the warnings about the tightness of the timetable, it is not yet too late.
Boris Johnson faces another deadline on Saturday - the date set out in the so-called Benn Act, which was passed last month by MPs seeking to avoid a no-deal Brexit.
If MPs have not approved a deal - or voted for leaving the EU without one - by Saturday, then Mr Johnson must send a letter to the EU requesting an extension to 31 January 2020.
The prime minister's official spokesman has confirmed the government will table a motion for Parliament to sit this Saturday from 09:00 to 14:00 BST.
That motion would be considered on Thursday.
However, this does not mean the House of Commons will definitely sit on Saturday - the government could table the motion but not push it to a vote.
The expectation on the EU side is that a new Brexit deal text is pretty much ready.
They are now just waiting to hear from the UK side whether it can be signed off.
Even if this text is ready, though, even if it can be signed off by EU leaders, the EU will not yet be breathing a sigh of relief because they have been here before.
Theresa May signed a Brexit deal with the EU and it went on to be rejected multiple times by House of Commons.
The fear is, if a new Brexit text meets the same fate, the UK government will come back to Brussels asking for more concessions.

Contingency plans in case the UK has to leave the EU with no deal in place are "well under way", a minister has said.
Dominic Raab said while the UK had to "strive for the very best outcome" from Brexit negotiations, it had to "prepare for all eventualities".
The Sunday Telegraph claimed there were plans to "unlock" billions of pounds in the new year to prepare for a "no deal" Brexit, if talks make no progress.
Six months of Brexit negotiations have not led to a significant breakthrough.
Last month Prime Minister Theresa May used a speech in Florence to set out proposals for a two-year transition period after the UK leaves the EU in March 2019, in a bid to ease the deadlock.
Talks had stalled over key issues including EU citizens' rights, a financial settlement and on the Northern Ireland border.
UK Brexit Secretary David Davis has since said "decisive steps forward" have been made - although EU Brexit negotiator Michel Barnier has said there are still "big gaps" between the two sides on some issues.
The Sunday Telegraph reported that, if no further progress is made, Mrs May has decided to commit billions in the new year to spend on things like new technology to speed up customs checks, in case there is no trade deal and the UK has to revert to World Trade Organisation tariffs with the EU.
Appearing on the BBC's Sunday Politics, Justice Minister Mr Raab was asked why there was no visible sign of preparations for no deal - such as the recruitment of more customs officers and more infrastructure at ports.
He said: "This planning goes on, it's right that it does because of the prime minister's clear point of view that we need to search and hope for the best, strive for the very best outcome from these negotiations, but prepare for all eventualities.
"What we don't do is run around advertising it demonstrably. Why? Because we want to send the right, positive tone to our EU partners.
"So we don't go talking about what happens if we end up with no deal, but quietly, assiduously, those preparations will be in place."
He added that the government wanted to see "the best deal I think in terms of trade, security, co-operation" but added: "Those contingency plans are well under way."
Labour's Shadow Foreign Secretary Emily Thornberry told the programme that after Brexit, Britain "should stay as close as we can" to the EU because it is "good for our economy".
"We need to leave the European Union but it is good for our economy - they're our biggest market - that we stay as close as we can.
"And the problem that the British country has is that a good half of the Tory party wants to go sailing off into the mid-Atlantic with no deal at all and that would be disastrous for our country."
EU leaders are due to decide at October's meeting of the European Council whether enough progress has been made on key issues to move on to the UK's post-Brexit relationship with the EU.
Meanwhile two Conservative MEPs who voted to block moves towards trade talks between the UK and European Union have had the party whip removed.
South West MEP Julie Girling and South East MEP Richard Ashworth were suspended from the Conservative Party after supporting a resolution in Strasbourg declaring that "sufficient progress" had not been made in talks to move on to discussions about the future relationship.
In a letter, European Parliament Chief Whip Dan Dalton said: "Given the seriousness of this issue, and your failure to discuss your intention to vote against the agreed position of the Conservative delegation in advance, I am therefore writing to inform you that I am suspending the Conservative whip from you until further notice."
Julie Girling told her local newspaper she had not voted to block trade talks but to "focus the minds of negotiators" and "drive more effective negotiations".
Mr Ashworth reportedly said he was confused by the suspension: "The vote was not about disrupting Brexit and the negotiations. We were asked a technical question about how much progress had been made and the answer for me was not enough."
The fourth round of Brexit negotiations began on 25 September, with the UK due to leave the EU in March 2019.

Donald Tusk has poured cold water on hopes of a Brexit breakthrough at Wednesday's EU summit, saying the Irish border was still a sticking point.
The European Council president said he had "no grounds for optimism" it would be solved at the summit.
And he called on Theresa May to come up with "concrete proposals" to break the "impasse".
The prime minister told her cabinet a deal was within reach if the government "stand together and stand firm".
Asked if she would be coming forward with "concrete proposals" at the summit, Mrs May's official spokesman said: "The prime minister set out her position yesterday (Monday). She looks forward to a face-to-face discussion with him tomorrow.
"There are many areas where we have made progress. More progress is needed on the backstop."
The "backstop" is a fall back plan for avoiding a hard border in Ireland if the two sides can't strike a trade deal in time - but they can't agree on how long it should last and what form it should take.
No new proposals are expected to be tabled or discussed this week and discussions are likely to continue at official level only.
Mrs May had already put forward a "workable solution", Downing Street said.
Speaking at a press conference in Brussels, Mr Tusk said: "As I see it, the only source of hope for a deal for now is the goodwill and determination on both sides.
"However, for a breakthrough to take place besides goodwill we need new facts.
"Tomorrow (Wednesday), I am going to ask Prime Minister May whether she has concrete proposals on how to break the impasse."
He urged Mrs May to present "something creative enough" to break the deadlock.
He said EU leaders would discuss how to step up preparations for a "no-deal scenario", but stressed that did not mean they were not also making "every effort to reach the best agreement possible for all sides".
Both sides in Brexit talks were hoping that a deal on the UK's withdrawal from the EU, including the Irish border question, would be agreed by mid-November in time for it to be ratified by EU members and for MPs at Westminster to vote on it.
The UK and the EU had hoped that enough progress would be made at Wednesday's EU council meeting to call a special summit in November to finalise the terms of the UK's exit.
Asked if the November summit would still go ahead, Mr Tusk said: "It's for the leaders to decide whether we need an extraordinary summit in November or not.
"Logistically, we are ready, but we need the feeling that we are close to a real breakthrough. The clock is ticking."
Downing Street said Mrs May has told cabinet ministers not to be "downhearted" if the European Council does not set a date for a November summit, amid growing expectation in government that any final agreement may be pushed back to December.
The prime minister told a cabinet meeting on Tuesday morning she could not agree to any deal with the EU which created a new border between Northern Ireland and the rest of the UK - or one which locked the UK into a customs union with the EU indefinitely.
She says this would be the consequence of the proposals currently on the table from the EU.
The cabinet had discussed a "mechanism" that would avoid an indefinite customs union if a full trade deal cannot be agreed by the end of the 21-month transition period that is due to kick in after the UK leaves on 29 March - the so-called "backstop" plan.
But it was "not a decision-making cabinet", Downing Street said.
However, the EU is considering a proposal for a UK-wide temporary customs arrangement, Mrs May's spokesman added.
The prime minister told ministers progress had been made in Brexit talks on the "future framework" for trade and although there would be challenging moments ahead a deal with Brussels was within reach, Downing Street said.
"I am convinced that if we as a government stand together and stand firm we will achieve this," she said.
Mrs May used Tuesday's cabinet to rally support for her position among senior ministers, amid reports eight of them had met on Monday to discuss their concerns about it.
Downing Street said none of the eight - Dominic Raab, Jeremy Hunt, Michael Gove, Penny Mordaunt, Chris Grayling, Liz Truss, Andrea Leadsom and Geoffrey Cox - had threatened to quit at Tuesday's cabinet meeting and it was clear that she had strong support.
The EU's chief Brexit negotiator Michel Barnier, who is travelling to Luxembourg to brief EU leaders ahead of Wednesday's summit, said he hoped a deal with Britain was possible "in the coming weeks".
"We are still not there.
"There are still several issues which remain unresolved, including that of Ireland, and therefore what I understand is that more time is required to find this comprehensive deal and to reach this decisive progress which we need in order to finalise these negotiations on the orderly exit of the United Kingdom."

Unless the UK's withdrawal agreement with Brussels is reopened and the backstop abolished there is no prospect of a deal, Downing Street has said.
The strong statement came after the EU pushed back against Boris Johnson's proposal to implement "alternative arrangements" for the UK-Irish border.
Mr Johnson has said the backstop is "anti-democratic" and must be scrapped.
European Council President Donald Tusk said it was "an insurance to avoid a hard border on the island of Ireland".
Meanwhile, the government has announced UK officials will stop attending most EU meetings from 1 September.
The Department for Exiting the European Union said it would "unshackle" them from discussions "about the future of the Union after the UK has left" and allow them to focus on "our immediate national priorities".
Later this week Mr Johnson will meet German Chancellor Angela Merkel and French President Emmanuel Macron for the first time since entering No 10.
Ahead of that, in a letter to European Council President Tusk, he called for the backstop to be removed from the withdrawal agreement reached between the EU and his predecessor, Theresa May, arguing it risked undermining the Northern Irish peace process.
Mr Johnson said the reaction to his demand for the backstop to be scrapped had been "a bit negative" but "we will get there".
He said he would enter Brexit talks with EU leaders with "a lot of oomph".
Mr Johnson added: "I think there is a real sense now that something needs to be done with this backstop. We can't get it through Parliament as it is."
He reiterated his view that EU countries were less likely to make concessions to the UK "as long as they think there's a possibility that Parliament will block Brexit".
The border is a matter of great political, security and diplomatic sensitivity, and both the UK and EU agree that whatever happens after Brexit there should be no new physical checks or infrastructure at the frontier.
The backstop is a position of last resort to guarantee that, but if implemented, it would see Northern Ireland stay aligned to some rules of the EU single market.
It would also involve a temporary single customs territory, effectively keeping the whole of the UK in the EU customs union.
Mrs May's withdrawal agreement has been voted down three times by MPs.
A series of voices from the European side rejected Mr Johnson's assertions.
Mr Tusk said those opposing the backstop without "realistic alternatives" supported re-establishing a hard border.
This was the reality "even if they do not admit it", he added.
The European Commission said Mr Johnson's letter did not contain a "legally operational solution" to prevent a hard Irish border.
"It does not set out what any alternative arrangements could be," a spokeswoman said, and "recognises that there is no guarantee such arrangements would be in place by the end of the transitional period".
Guy Verhofstadt, Brexit spokesman for the European Parliament, said the backstop was "a vital insurance policy... supported by the people of the island of Ireland".
And speaking in Iceland, Chancellor Merkel said: "Once we have a practical solution to ensure that the Good Friday Agreement continues to apply, then we don't need the backstop of course."
A Downing Street spokesperson insisted the UK government was "ready to negotiate, in good faith, an alternative to the backstop, with provisions to ensure that the Irish border issues are dealt with where they should always have been: in the negotiations on the future agreement between the UK and the EU".
The question is whether Boris Johnson's letter to the EU is intended as the start of negotiations - or designed to be the end of them.
He's suggested the only way to get a deal is to take the backstop out. Not to time limit it, or modify it, but to bin it.
But if he has a fully-fledged, different plan up his sleeve, why he isn't spelling out more detail of those "alternative arrangements"?
And why can't Downing Street say what additional reassurances would be available to the Irish government in the absence of a backstop, if trade talks falter?
The lack of detail on Plan B has made some critics in his own party wonder if his Plan A is simply to make an offer the EU can't accept and then blame them for no deal.
But No 10 insists he'd do a deal quickly if the EU was more flexible. In other words, Brussels would be expected to blink first as the prospect of no deal approaches.
So far, though, the EU is staring him out.
Labour leader Jeremy Corbyn said it was unclear what the prime minister thought he was negotiating.
"He needs to recognise that by just holding the threat of a no-deal Brexit on 31 October towards the European Union isn't going to bring about a change, it's going to make things much worse," he said.
"He created this arbitrary date by his behaviour during the Tory Party leadership campaign. He needs to wise up and stop the nonsense of 31 October and start talking seriously."

Parliament has a "clear choice" to stand up for the UK against a draft Brexit deal or allow it to break up the union and make the UK a "vassal" state, DUP MP Nigel Dodds has said.
The Irish border has been the main sticking point in the talks.
The UK and EU have agreed to a "backstop", which would see NI stay aligned to some EU rules if another solution cannot be found.
Mr Dodds told MPs the prime minister had broken promises made to his party.
Several cabinet ministers have resigned, saying the deal presents a threat to the integrity of the union.
Mr Dodds was among MPs criticising the prime minister in the House of Commons amid a backlash over her plan.
The DUP's 10 MPs prop up the Conservative government to ensure it has a majority to pass key legislation in the Commons.
Mr Dodds said he could take Mrs May through the list of promises she made about the future of Northern Ireland but that would be a "waste of time because she clearly doesn't listen".
He put it to MPs: "The choice is now clear, we stand up for the United Kingdom, the whole of the United Kingdom, the integrity of the United Kingdom or we vote for a vassal state with the break-up of the UK."
But the prime minister said it was wrong to imply that she had not considered the interests of the people of Northern Ireland.
The real spat among politicians is over the UK and EU's agreement on the Northern Ireland backstop.
It would see Northern Ireland staying aligned to some rules of the EU single market, if another solution cannot be found by the end of the transition period in December 2020.
That means that goods coming into Northern Ireland would need to be checked to see if they meet EU standards.
It would also involve a temporary single custom territory effectively keeping the whole of the UK in the EU customs union - until both the EU and UK agree that it is no longer necessary.
Mrs May has said there was no deal on the table that did not involve signing up to the backstop - but that it is only an insurance policy.
"I know there are some who said I should simply rip up the UK's commitment to the backstop but this would have been an entirely irresponsible course of action," she said.
Labour has also said it will not approve the plan, with party leader Jeremy Corbyn saying the backstop proposal would create a "de facto border in the Irish Sea".
Mr Corbyn said it locked "Britain into a deal which it cannot leave without the agreement of the EU".
Yes, four resignations by junior and cabinet ministers before 10:30 GMT on Thursday, including the Brexit Secretary, Dominic Raab.
The DUP's deputy leader, Nigel Dodds, tweeted thanks to Mr Raab and others for "standing up for the union".
Karen Bradley has denied accusations that the political fall-out over the draft Brexit plan is a "car crash" and said the deal was "good for the union".
She was speaking in Belfast after meeting a number of business leaders to discuss what has been agreed by EU and UK negotiators.
"Nobody said it would be easy," said Mrs Bradley, adding that the majority of the cabinet is still behind the deal.
She gave Mrs May her full support, and said: "This is a woman who gets things done."
The Northern Ireland Secretary also appealed for "cool heads".
"The people of Northern Ireland when they see this deal will see it is a good deal for the whole of the UK and Northern Ireland, and I hope they tell their politicians that," she added.
Asked about whether there are question marks over the future of the government's confidence and supply deal with the DUP, Mrs Bradley said that was a "matter for the parties' chief whips".
Mrs May has faced a huge backlash from the Democratic Unionist Party (DUP), amid suggestions of moves within the Conservative Party to force a no-confidence vote.
DUP MP Jim Shannon said his party had been "betrayed" by the prime minister.
He told BBC NI's Good Morning Ulster programme that his party feels Theresa May has broken her commitments to them and is "up for an election".
Stephen Farry, the deputy leader of Alliance said it is important that the business community speaks out more loudly in the coming days, as the deal offers them the best of both worlds.
You can But Ulster Unionist leader, Robin Swann, said the draft deal had been "a monumental error of judgement on behalf of the DUP", which would have a devastating long-term impact.
The Irish Foreign Minister, Simon Coveney, has said people "should not talk down" the chances of a Brexit deal getting through Parliament.
Mr Coveney told Irish national broadcaster RTÉ that the deal is "the only one on the table".
An emergency EU summit is now due to take place on 25 November to agree the draft text.
After that, Mrs May needs to get MPs to vote for it. The BBC's political editor Laura Kuenssberg said that could take place in early December.
There have been a number of calls by senior Conservatives for the prime minister to go and there could yet be more resignations from the cabinet.
Former chairman of the Northern Ireland Affairs Committee Laurence Robertson sa