Cabinet ministers are openly at war over solving the Brexit crisis, after MPs were threatened with a general election if they try to force through an alternative to Theresa May’s deal.

As claims of a plot to topple the prime minister were denied by potential replacements, a bid by the Commons to seize control this week was dramatically torpedoed by the Brexit secretary.

Stephen Barclay vowed that any softer exit plan that crossed Tory red lines would be rejected, warning MPs tempted to vote for it that “the risk of a general election increases”.

Extraordinarily, just moments earlier, the chancellor Philip Hammond had urged MPs of all parties to “get themselves together in a room” to find a solution, admitting Ms May’s deal is all but dead.

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Meanwhile, a parade of Brexiteer Tories drove to the door of Chequers, the prime minister’s country retreat, some to urge her to set a timetable for quitting.

However, as both the mooted candidates to take over as caretaker – David Lidington and Michael Gove – rushed out denials of interest, no cabinet coup appeared imminent.

Despairing Tories feared the prime minister would not listen to pleas that the only way to save her deal is to fall on her sword immediately afterwards. Others believe it would fail to make the difference anyway.

The guest list for the emergency Chequers summit drew criticism that Ms May was still turning to an “an old boys club”, rather than listening to different voices on Brexit.

Downing Street sources said the aim was still to win backing for a third “meaningful vote” on the Brexit deal this week, although Ms May herself has said it could be pulled.

A spokesperson for the prime minister said: “The PM and a number of government ministers met today at Chequers for lengthy talks with senior colleagues about delivering Brexit.

“The meeting discussed a range of issues, including whether there is sufficient support in the Commons to bring back a meaningful vote this week.”

Mr Lidington, Ms May’s de-facto deputy, was also in attendance, after denying a plot by saying: “I don’t think that I’ve any wish to take over from the PM [who] I think is doing a fantastic job.”

Jacob Rees-Mogg and his eldest son Peter arrive at Chequers (LNP)

Likewise Mr Gove, the environment secretary, said before heading to Chequers: “This is a time for cool heads. It’s not the time to change the captain of the ship.”

Many questioned how a caretaker could be imposed, given that – under the Fixed Term Parliaments Act – he or she would need the backing of the entire Tory party to win a no-confidence motion in the Commons.

The next twist in the Brexit drama will be a cross-party attempt on Monday to grab the Commons floor on Wednesday, to stage so-called “indicative votes” on all options, to try to find a “winner”.

Some ministers had suggested free votes for all Tory MPs, including ministers, to truly open up debate, but Mr Barclay stamped on the process in a BBC interview.

He made clear a result would be rejected if it were to “collide with fundamental commitments the government has given in its manifesto” – which included leaving the EU customs union and single market.

MPs trying to legislate for such a dramatic shift in UK policy would also be triggering a longer Brexit delay, requiring participation in the European parliament elections.

“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,” Mr Barclay said.

The threat was angrily dismissed as “nonsense” by Nick Boles, a pro-EU Tory behind the “Common Market 2.0” plan for a softer Brexit, by retaining single market membership.

“The PM cannot call a general election whenever she feels like it,” he tweeted. “She would need the backing of 2/3 of MPs. No way that most Tory MPs are voting for an early election.”

Mr Boles condemned the refusal of European Research Group hardliners to “compromise with reality”, adding: “They can’t impose hard Brexit because they don’t have the votes. They can’t force an election because they don’t have the votes.”

On the Labour side, Keir Starmer strengthened the party’s backing for a Final Say referendum – despite, like Jeremy Corbyn, failing to attend Saturday’s march.

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“If a deal goes through, if the prime minister’s deal, if she tries it a third time, goes through, it ought to be subject to a lock or a check, which is it’s got to be confirmed by the public,” he said.

The prime minister will host a cabinet meeting on Monday morning, ahead of a testing statement to the Commons on the EU’s imposition of a new Article 50 deadline at last week’s summit.