MPs have failed to unite around any Brexit strategy after a series of indicative votes revealed no majority in the Commons for any plan.
Attempts to break the Brexit impasse floundered when MPs rejected eight different options, including a fresh referendum, a customs union and a no-deal exit.
In a dramatic day in Westminster, Theresa May told Tory MPs she will resign before the next phase of Brexit talks, in an attempt to secure support for her deal.
Addressing the 1922 committee of backbench Conservatives, the prime minister said she “would not remain in post for the next phase of the negotiations”, making way for a successor once her Brexit deal has passed.
Senior Brexiteers including Boris Johnson and Iain Duncan Smith signalled they would pivot to back the prime minister’s deal – but the DUP dealt Ms May a fresh blow by refusing to support her.
But it seems her offered sacrifice may have been in vain, as the Democratic Unionist Party announced it would not back a deal which “poses an unacceptable threat to the integrity of the United Kingdom”.
In a potentially fatal blow to Ms May’s chances, DUP leader Arlene Foster said the Northern Irish party “cannot sign up” to the deal because of its controversial “backstop” provisions.
Westminster leader Nigel Dodds made clear the party’s 10 MPs will vote against the deal if it is brought back for a third “meaningful vote”, declaring: “The DUP do not abstain on the Union.”
The decision leaves Ms May in need of the votes of large numbers of Labour MPs or rebel Tory Brexiteers, many of whom are expected to be strongly influenced by the DUP’s stance.
She has indicated she will only make a third attempt to pass the deal, following its overwhelming defeat by 230 votes in January and 149 in March, if she has a credible chance of success.
Follow along with our coverage of how the day unfolded
"He will order MPs to vote for this. We had a really constructive process of engaging with him. At no point was he instinctively against this," Mr Kyle told the BBC Radio 4 Today programme.
Moments, later Barry Gardiner, the shadow international trade secretary, cast doubt on the position.
"What it says in that amendment is that any deal should be subject to a second public vote," Mr Gardiner told Sky News.
"That would mean even if our preferred option of a new customs union and an alignment of rights were to get through, that would also perhaps be knocked out by a second public vote. That has not been our party's position so far," he added.
If on Monday one or more propositions get a majority backing in the House of Commons, then we will have to work with the Government to implement them.
The way I would hope it would happen under those circumstances is that we would have sensible, workmanlike discussions across the House of Commons and the Government would move forward in an orderly fashion.
If the Government didn't agree to that, then those who I am working with across the parties will move to legislate to mandate the Government - if we can obtain majorities in the House of Commons and House of Lords for that - to carry that forward."
Jean-Claude Juncker and Donald Tusk are addressing the European Parliament,
Speaking in Strasbourg, Mr Tusk said the EU should be "open to a long extension".
Before the European Council I said we should be open to a long extension if the UK wants to rethink its Brexit strategy, which would of course mean the UK's participation in the European Parliament elections.
Then there were voices saying that this would be harmful or inconvenient to some of you: let me be clear, such thinking is unacceptable.
You cannot betray the six million people who signed a petition to revoke Article 50, the one million people who marched for a people's vote, or the increasing majority of people who want to remain in the European Union.They may feel that they are not sufficiently represented by the UK parliament but they must feel that they are represented by you in this chamber because they are Europeans."

EU president warns against 'betraying' Remain voters who are 'not represented by UK parliament'
Anti-Brexit British voters who want to remain in the EU must not be "betrayed", the president of the European Council has warned. Donald Tusk said many of the millions of people who had signed a petition to revoke Article 50 or who had marched against Brexit at the weekend might feel that they "are not sufficiently represented by the UK parliament". He said it was the duty of
Labour does not back revoking Article 50, says Corbyn ally Barry Gardiner
Party will also not support revoking Article 50, shadow cabinet minister saysMrs Leadsom told BBC Radio 4's Today programme:
I think that there is a real possibility that it does. We are completely determined to make sure that we can get enough support to bring it back.
The Prime Minister said she is working hard, as many colleagues are, to persuade colleagues to support it."
Mrs Leadsom refused to be drawn on whether Theresa May should commit to standing down once the Withdrawal Agreement is passed in order to win over wavering MPs.
"I am fully supporting the Prime Minister to get us out of the European Union," she said.
Asked if Mrs May should stand down after that, she said: "I think that is a matter for her. I am not expressing a view."
I haven't changed my mind about the deal - it is still a bad deal and doesn't properly deliver Brexit. The risk is, if I don't back it, we don't leave the EU at all."
The European Council president told the European Parliament: "Let me be clear, such thinking is unacceptable.
"You cannot betray the six million people who signed the petition to revoke Article 50, the one million people who marched for a people's vote, or the increasing majority of people who want to remain in the European Union.
"They may feel that they are not sufficiently represented by their UK Parliament, but they must feel that they are represented by you in this chamber because they are Europeans."
We ought to be leaving on Friday at 11 o'clock with or without a deal but that's not the situation we find ourselves in.
They (MPs) didn't like the result, they thought the British people have got it wrong, that's what today is all about."
After he said the party could not support an amendment linking the Brexit deal to another referendum:
He told the European Parliament: "You know what the problem is? The problem of the humiliation and punishment is because of the mess in the Tory Party - there is the humiliation of the British people."

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Nigel Farage compares Brexit deal to Treaty of Versailles that helped Hitler rise to power
Former Ukip leader makes outlandish claims of 'reparations' and 'annexations'Theresa May could bring back her Brexit deal to the Commons this week amid signs growing numbers of Tory rebels are now ready to back it, a senior Cabinet minister has said.
Leader of the House Andrea Leadsom said there was a "real possibility" there would be sufficient support for the Government to stage a third "meaningful vote", either on Thursday or Friday.
She said ministers were continuing to talk to MPs - including those in the DUP, who prop up the Government at Westminster and whose votes may be crucial in determining the outcome.
Mrs Leadsom told BBC Radio 4's Today programme: "I think that there is a real possibility that it does (come back).
"We are completely determined to make sure that we can get enough support to bring it back."

EU's chief Brexit negotiator says UK 'can stay'
Barnier says anything is possible until just before planned exit date of 12 AprilPlease allow a moment for the live blog to load