Theresa May faces a Brexiteer backlash over the plans agreed by her Cabinet at Chequers.

The Prime Minister said the strategy thrashed out with the Cabinet would make sure Brexit was delivered “because I won’t let people down”.

But backbench Tory Brexiteers hit out at the plans, with speculation at Westminster that some could be prepared to submit formal letters calling for a leadership contest.

Meanwhile, it emerged that Foreign Secretary Boris Johnson backed the proposals at Chequers despite claiming that defending the plans was like “polishing a turd”.

Despite his reservations, Mr Johnson fell into line along with the rest of the Cabinet’s Brexit-backing ministers.

The fallout has continued from the Chequers meeting where the Cabinet agreed the Brexit strategy (Joel Rouse/Crown Copyright/PA)
The fallout has continued from the Chequers meeting where the Cabinet agreed the Brexit strategy (Joel Rouse/Crown Copyright/PA)

Tory MP Andrew Bridgen compared the Foreign Secretary to Neville Chamberlain, accusing him of “waving the white flag of appeasement in the direction of Brussels”, along with other Brexiteer ministers.

Meanwhile, the Sunday Times reported that in a draft leadership letter circulating in Westminster, rebel Tories accuse the Prime Minister of letting the negotiations with Brussels descend “into a state of complete capitulation”.

It claims the Prime Minister’s Brexit promises appeared to be “a pretence and a charade intended to dupe the electorate” and concludes that “in the interests of our country and the future of the Conservative Party, I feel the time has come for a new leader”.

Mr Bridgen, writing in the Mail on Sunday, said Jacob Rees-Mogg – leader of the pro-Brexit European Research Group – was now the only credible challenger to Mrs May after the failure by Cabinet ministers to oppose the Chequers plan.

In a message to the Cabinet, he said: “All those harbouring leadership hopes have done their ambitions fatal harm.

“Grassroots party members will have no truck with their perceived treachery.

“Some will try to keep their leadership hopes alive by claiming it was not the time to quit and they had a duty to stay on to ensure Brexit is not further watered down.

“But it leaves only one credible contender with the integrity and backbone to follow Mrs May: Jacob Rees-Mogg.”

But Mrs May told the Sunday Times:  “The only challenge that needs to be made now is to the European Union to get serious about this, to come round the table and discuss it with us.”

The Prime Minister will address Tory MPs on Monday and her chief of staff Gavin Barwell has been engaged in efforts to explain the Chequers deal to concerned colleagues alongside Chief Whip Julian Smith.

Former Tory leader Iain Duncan Smith told the Sunday Telegraph the Chequers plan appeared to amount to “continued membership” of the customs union and single market for goods despite the Prime Minister’s promise to leave both.

“If the public perceive that not to be delivered then the Government, I’m afraid, will suffer the consequences at the next election,” he said.

Mr Rees-Mogg warned that “a very soft Brexit means that we haven’t left, we are simply a rule-taker”.

“That is not something that this country voted for, it is not what the Prime Minister promised,” he told BBC Radio 4’s Today.

An analysis of the Chequers statement circulating within the ERG was damning about the plans.

The Chequers proposals “lead directly to a worst-of-all-worlds ‘black hole’ Brexit where the UK is stuck permanently as a vassal state in the EU’s legal and regulatory tarpit”, the briefing by Martin Howe QC concluded.

The document has not been endorsed by the ERG but was “devastating”, a Brexiteer source said.

The plans agreed at Chequers would create a new UK-EU free trade area for goods, with a “common rulebook”.

A new “facilitated customs arrangement” would remove the need for checks at the Irish border and ports, treating the UK and EU “as if a combined customs territory”.

Tories who attended the first briefing organised by Downing Street on the plans said their concerns had been met, and Mrs May will hope that restive Brexiteers also fall in line when they hear more about the proposals which will be set out in a white paper on Thursday.

James Cleverly, a deputy chairman of the party who attended the Saturday morning briefing, said: “I went in there with some concerns as a Brexiteer and I come out with those concerns addressed.”

He said the briefings “will massively calm the nerves of people who have been basing their views on the speculation that has been floating around in the media and social media”.

The Prime Minister told the BBC: “We’re leaving the European Union. I think when people voted to leave the European Union, they wanted an end to free movement – free movement will end.

“They wanted us to end the jurisdiction of the European Court of Justice in the UK – that will end.

“They wanted us to stop sending the vast sums of money every year to the EU that we do today, and so take control of our money, our laws and our borders – and that’s exactly what we will do.

“But we’ll do it in a way that protects drops and enhances our economy for the future.”