The plan, agreed by ministers after 12 hours of closed talks at Chequers on Friday, provoked a furious backlash among Brexiteer MPs, who claim it keeps Britain too closely aligned with the EU and is “hugely damaging” to the reputation of the prime minister and her party.
As the fallout intensified, Tory MPs began circulating a draft letter accusing Ms May of “complete capitulation” and saying “the time has come for a new leader”.
Some Conservative MPs told The Independent they believed there could be enough disgruntled MPs willing to trigger a leadership contest in a bid to remove Ms May.
But even if the 48 needed to oust Ms May materialised, a poll for The Independent showed a majority of the public would expect a general election to be called if Ms May goes.
And with Labour suggesting it would not back the government’s plan, speculation mounted over the prime minister’s ability to get parliament to approve the final deal she negotiates with Brussels.
The prime minister is set to face an angry backlash over the Chequers agreement when she addresses her party at a meeting of the 1922 Committee of Tory MPs on Monday night.
The plan would see the UK effectively stay in the single market for goods, giving the European Court of Justice an ongoing say over British rules.
That is anathema to many Brexiteers, who believe Ms May has broken her promise to remove the UK from the single market entirely.
They are also concerned that ministers are considering giving EU citizens preferential rights to come to the UK.
With Eurosceptic Tories lining up to condemn the plan, speculation mounted that many were ready to write to Graham Brady, chair of the 1922 Committee, to request a leadership election. Under Conservative Party rules, 48 letters are needed to trigger an contest.
One Eurosceptic MP told The Independent they believed there could be enough support for a challenge.
“The disappointment is so great that there may well be enough letters,” the MP said. “There is considerable concern and disappointment on the back benches.”
And Sir Bill Cash, a senior Brexiteer, warned Ms May it would not be difficult to trigger a leadership contest. He told Sky News: “If people were to decide to put in those letters, you only need 48.”
Government whips are understood to have been phoning Tory MPs over the weekend in a bid to talk them round, but some are so angry that they are not even willing to engage in discussion.
However, other Tories dismissed the Brexiteers’ threats, saying they have threatened to topple Ms May on previous occasions.
One MP said: “The threats are empty. It’s all bollocks. It’s all crap. Nothing will happen. Nothing has changed. It is all balls. What they’ll do is what the group always does, which is threaten. I don’t think their threats are valid but some people will be scared by it and that will have an impact.”
MPs said much will depend on what Jacob Rees-Mogg, leader of the European Research Group of Eurosceptic Tories, decides to do.
The Brexiteer ringleader has criticised the Chequers plan but said he will await further details, due in a government white paper to be published this week, before deciding what action to take.
Referring to some other Brexiteers, one MP said: “Nobody takes these people seriously. Who will be quite an important figure is Jacob because people do take Jacob very seriously.
“If Jacob decided to say, for example, that he was withdrawing support for the prime minister, that would be a significant political moment.”
Facing down her critics, Ms May dismissed talk of a leadership challenge.
She 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.”
And some Tories suggested that, even if there were to be a leadership challenge, Ms May could stand again and win – possibly without anyone else throwing their hat in the ring.
One said: “Fundamentally the prime minister is the prime minister and leader of the party because there is nobody else who people think would be better at that job. There is nobody.
“Nothing happened this last weekend that has changed that fact.”
Another, who is not a supporter of Ms May, said: “No 10 think that because they’ve tied the cabinet in with the deal, there will no challengers and the prime minister will just carry on.
“At the moment most of the potential leadership challengers are tied in. She’s actually squeezed the credibility out of them all.”
Andrew Bridgen, one of the most vocal Tory critics of the Chequers agreement, claimed some senior Brexiteers are hesitant to speak out because they think the EU will reject the government’s plan, meaning it is unlikely to ever become a reality.
“Some very senior Eurosceptic colleagues believe we’re OK – we won’t have to kick up a fuss because the EU won’t accept it,” he said. “I wouldn’t like to rely on that.”
He also predicted the Chequers plan would be “hugely damaging” to Ms May and the Conservative Party, saying: “We’ve already seen a dip in the polls immediately and I think that’s going to get a lot worse.
“This is going to be hugely damaging to the poll ratings of the government and it is going to be hugely damaging to the prestige and reputation of the prime minister. I am hoping that we’re going to pull back from the abyss.”
He added: “I feel that we’ve let the country down badly.”
Asked what action he intended to take, Mr Bridgen replied: “I’m going to give the prime minister the benefit of hearing what she’s got to say at the 1922 [Committee], and following that I will take whatever steps I feel are appropriate.”
The pressure on Ms May grew as Labour suggested it would not back a Brexit deal based on the government’s current strategy. If enough Tory Brexiteers rebel, that could make it difficult for the prime minister to secure MPs’ backing for the agreement she negotiates with Brussels.
Shadow Brexit secretary Sir Keir Starmer told the BBC’s Andrew Marr Show: “She hasn’t met our demands. We’ve been clear you need a comprehensive customs union and you need a single market deal with shared institutions and shared regulations.
“She’s come up with a fudge on customs. It is a fudge and it’s going to unravel. She’s going to have to think again.”
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