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Boris Johnson has branded Theresa May’s Brexit deal “dead” amid calls for the Prime Minister to honour her commitment to step down even if Parliament rejects her blueprint again.

A ministerial source said Mrs May is determined to put the twice-rejected withdrawal agreement to a third vote, possibly as early as tomorrow, despite her DUP allies publicly opposing it.

It emerged this morning that former foreign secretary Mr Johnson, who pivoted behind the Prime Minister’s deal last night only after she made clear she will resign from No 10 once it is through, has told friends: “It’s dead anyway.”

Mark Francois, vice-chairman of the European Research Group of Tory Brexiteers, told BBC TV: “I told my whip the other day I wouldn’t vote for it if they put a shotgun in my mouth.”

Andrew Bridgen, an ERG backer, said Mrs May and her deal should both go. “Her authority is gone now,” he said.

“Whatever her solution is, how can she be part of it when all along she was the problem?” He said the parliamentary maths meant her deal stood no chance: “Twenty Conservatives and the DUP are not going to vote for it. It is not going to go through.”

Dominic Raab, the former Brexit secretary who is expected to stand for the Tory leadership in a summer contest, said the Government should “go back to the EU again” and ask for a legally binding exit from the backstop.

Former chief whip Andrew Mitchell revealed speculation on the leadership battle is building, telling the BBC that “quite a lot of colleagues are pressing” former Brexit secretary David Davis to stand.

An option being considered by No 10 in an attempt to win a third vote is to bring back the withdrawal agreement without the political declaration, which sets out future trade relations.

In an interview with the Evening Standard, Foreign Secretary Jeremy Hunt revealed that he thinks the EU might be flexible with its deadline for the deal if the Government decides to wait until next week for a final vote.

But the DUP appeared to be as firm as ever. In a statement at 10.25am on Twitter, the party said: “Back in December 2017 we warned about the dangers of the backstop. We cannot sign up to something that would damage the Union.”

One of Mrs May’s oldest allies, former de facto deputy prime minister Damian Green, predicted: “[Mrs May] will take the path of soldiering on because she sees the great duty of her and her Government is to get a Brexit deal.” He warned Brexiteers: “If you want a deal, the choice is now between the Government’s deal or a customs union. The customs union was only eight votes off winning yesterday.”

Sir Oliver Letwin, the architect of the inconclusive indicative votes staged yesterday on Brexit, warned the UK could be heading for a no-deal break on April 12 unless MPs back either Mrs May’s deal or an alternative such as a Commons Market 2.0 or customs union.

“At the moment we are heading for a situation where, under the law, we leave without a deal on the 12th,” he told BBC Radio 4’s Today programme. “At some point or other we either have to get her deal across the line or accept that we have to find some alternative.”

Belgian MEP Philippe Lamberts agreed that if the UK cannot ratify the withdrawal agreement and has “no new plan” by April 12, Brussels is ready to see Britain leave without a deal.

“That’s the state of mind in Brussels,” said Mr Lamberts, who sits on the European Parliament’s Brexit steering group. “Both in the European institutions and the member states, people have come to realise that, in absence of a positive majority in the UK, the by-default result will be a no-deal Brexit.

“We don’t like it, but you have to prepare for things that you don’t necessarily like.”

Eight options for handling Brexit were put to MPs yesterday but none found a majority. A customs union came closest.

ERG chairman Jacob Rees-Mogg left confusion over his voteafter creating headlines by indicating he would back Mrs May.

Last night he told the Peston show on ITV: “I’ve said I will support the DUP if the deal is brought back and they are still opposing it.” But this morning he told reporters: “I’m in favour of the deal and I hope the DUP will come over to the deal but we’ll have to wait and see what they do.”

Labour former foreign secretary Dame Margaret Beckett, who tabled a motion calling for any Brexit deal to be put to a “confirmatory” referendum, said MPs now need to be prepared to compromise. “They are going to have to look over the abyss,” she told Today.

Former Attorney General Dominic Grieve said he saw no advantage to Mrs May quitting if her deal gets through.

He told Sky News: “It seems to me that the likelihood is that if she does stand down when this deal has got through, the Conservative Party will tear itself apart because it’s quite apparent to me that there are a large number of colleagues who are seeking her departure, having got the deal across the line, solely for the purpose of then ripping the deal up and that is not a good way to proceed.”