Mrs May’s de-facto deputy David Lidington was forced to deny reports that he was being lined up to succeed her, with ministers Michael Gove and Jeremy Hunt also named as possible interim Tory leaders.

With MPs set to mount a bid to take control of the House of Commons order paper today and force votes on alternative Brexit plans, Chancellor Philip Hammond cast doubt on the Government’s ability to ever pass its own agreement with Brussels.

Mr Hammond also became the first Cabinet minister to suggest a second EU referendum could take place, saying it was a “perfectly coherent position” for MPs to consider.

Mrs May is reportedly facing pressure from within the Conservative party to quit over her handling of the Brexit process. Picture: Taylor/Getty Images

As speculation about a leadership coup reached fever pitch, Mr Lidington, the Cabinet Office minister, said: “I don’t think that I’ve any wish to take over from the PM, who I think is doing a fantastic job.

“I tell you this: one thing that working closely with the Prime Minister does is cure you completely of any lingering shred of ambition to want to do that task.I have absolute admiration for the way she is going about it.”

The Sunday Times reported that 11 Cabinet ministers want Mrs May to make way for someone else and that Mr Lidington was in line to take over.

But the Mail on Sunday said Brexiteer ministers were plotting to install Mr Gove, the Environment Secretary, as a caretaker leader.

Mrs May’s former policy adviser, MP George Freeman, said it was “all over for the PM”, tweeting: “She’s done her best. But across the country you can see the anger.

“Everyone feels betrayed. Government’s gridlocked. Trust in democracy collapsing. This can’t go on.”

Tory backbencher Anne-Marie Trevelyan wrote in the Sunday Telegraph: “We now need a leader who believes in our country and wants to take her on the next stage of her journey.”

As she tries to cling on to her job at the start of a decisive week for both her deal and for opponents seeking to stop Brexit, the Prime Minister met backbench Brexiteers at her country retreat.

Boris Johnson, Dominic Raab, Jacob Rees-Mogg, David Davis, Iain Duncan Smith and Steve Baker were all invited for talks at Chequers yesterday.

Mr Hammond accused MPs allegedly trying to oust the Prime Minister of being “self-indulgent”. He told Sky’s Ridge on Sunday programme that replacing Mrs May would not “solve the problem”.

But he risked adding fuel to the divisions among the Conservatives by saying a second EU referendum “deserves to be considered along with the other proposals” put to a vote this week.

“One way or another, Parliament is going to have the opportunity this week to decide what it is in favour of, and I hope that it will take that opportunity – if it can’t get behind the Prime Minister’s deal – to say clearly and unambiguously what it can get behind,” he said.

And with Downing Street still refusing to commit to bringing its own Brexit deal back to the Commons, Mr Hammond was downbeat about securing enough votes to pass it, saying: “I’m realistic that we may not be able to get a majority for the Prime Minister’s deal and if that is the case then Parliament will have to decide not just what it’s against, but what it is for.”

Brexit Secretary Steve Barclay raised the prospect of a general election if MPs take control of parliamentary proceedings and try to force through a Brexit that is at odds with government policy.

Mr Barclay said a “constitutional collision” in a series of “indicative votes” on alternative Brexit plans could result in a snap vote.

A series of votes on up to seven Brexit outcomes – including revoking Article 50 and holding a second EU referendum – are expected by Wednesday, with backbenchers and government ministers proposing them as a solution to the deadlock.

But Mr Barclay told the BBC’s Andrew Marr show: “If an amendment goes through where Parliament takes control of the order paper, then that leaves open the door to Parliament then legislating to take no-deal off the table.

“And that is something that Brexiteers like me would see as a massive risk to Brexit because if Brexiteers and Parliament votes against the deal and also votes to take no-deal off the table then the only option is to then have European parliamentary elections.”

Mr Barclay said if the Commons takes control of the order paper and votes for a different outcome, it would “potentially collide with fundamental commitments the Government has given in their manifesto”, though he said the vote itself would not be binding.

He said: “What Parliament has done is vote for a number of contradictory things so we would need to untangle that but ultimately, at its logical conclusion, the risk of a general election increases because you potentially have a situation where Parliament is instructing the executive to do something that is counter to what it was elected to do.”

Meanwhile a parliamentary petition calling for Article 50 to be revoked reached five million signatures.

The SNP’s leader at Westminster, Ian Blackford, said his party would back attempts to impose indicative votes on the Government.

“It would be an assault on democracy if Theresa May chooses to ignore the will of Parliament on this week’s Brexit votes,” he said.

“The Prime Minister has completely lost control of the Government, her own MPs and this Brexit process. It’s time for Parliament to take charge and put an end to this shambles.”

Theresa May faces her Cabinet amid speculation of coup plot