Up to 25 government members could vote for delay rather than allow UK to crash out

Theresa May is facing the most serious cabinet revolt of her premiership next week, with as many as 25 members of the government ready to vote for a Brexit delay unless she rules out “no deal” – in a move that will challenge her to sack them.

Rebel Conservatives believe there are now enough MPs across the House of Commons to pass an amendment that would require May to extend article 50 rather than allow the UK to leave without a deal.

At least four cabinet ministers, almost a dozen junior ministers and many others on the government payroll are understood to be prepared to back the motion proposed by the Tory MP Sir Oliver Letwin and Labour’s Yvette Cooper, due to be debated on Wednesday. A senior source close to those plotting the rebellion said there was no way the members of the government would resign voluntarily and May would have to sack them.

The move comes with moderates emboldened by the formation of the Independent Group, which some see as providing leverage to push back against the influence of the European Research Group of hardline Brexiters.

The cabinet ministers David Gauke, Amber Rudd, Greg Clark and David Mundell told the prime minister in a private meeting earlier this week that she would have to delay Brexit if there was no Commons majority for her deal by 27 February.

Speaking in Edinburgh on Thursday, Mundell told an audience he would do “everything I can and whatever I deem necessary to prevent a no-deal Brexit”, and refused repeatedly to rule out resigning from the cabinet if necessary.

May has already survived two rounds of resignations by the Brexit-supporting cabinet ministers David Davis, Boris Johnson, Esther McVey and Dominic Raab, but a wave of sackings would plunge the government into crisis at a crucial time for the Brexit talks.

Pro-Brexit MPs said the outcome of next week was unpredictable but, if it came to the vote, May would have to get rid of the rebellious ministers.

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One cabinet source said: “It would be a huge mistake not to sack them. It would be effectively conceding we had lost control of the party.”

To avert a crisis, No 10 is racing to secure changes to May’s withdrawal deal with the EU that will satisfy hardline Eurosceptics and the Democratic Unionist party, enabling parliament to approve it. Their central demand is the removal of the Irish backstop from the text of the agreement because it could indefinitely bind the UK into a customs union.

Downing Street sources said the prime minister ideally wanted to hold a parliamentary vote and win approval for her deal early next week, but sources conceded time was running out to pull off such a move.

She is heading to a meeting of world leaders, including the German chancellor, Angela Merkel, in the Egyptian resort of Sharm-el-Sheikh at the weekend in a last-minute effort to break the deadlock. The key to the talks is whether they can find a solution to allow Geoffrey Cox, the attorney general, to change his legal advice that the backstop is indefinite. However, Jean-Claude Juncker, the European commission president, told reporters in Brussels he was “not very optimistic” about the progress of talks so far.

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“If a no-deal would happen – and I can’t exclude this – this would have terrible economic and social consequences, both in Britain and on the continent, and so my efforts orient in a way that the worst can be avoided,” he said.

If May does not manage a breakthrough by Wednesday, several senior cabinet ministers are pushing her to give assurances from the dispatch box that she is so close to a withdrawal deal that there is no need to consider the possibility of Brexit without one any more. “If you think you can get a deal with the EU by early April, what’s the point of crashing out on 29 March?” said one source close to the rebels.

However, that strategy risks infuriating the DUP and hardline Eurosceptics, many of whom favour a no-deal Brexit and would want to see the text of an agreement with the EU before removing that possibility.

One option for May is to call a free vote, which is the solution favoured by the “Brexit delivery group” of 100 MPs from both the remain and leave wings of the party. They have warned her that many of their number are prepared to rebel unless she allows MPs to vote with their consciences.

Three MPs in the ERG – Priti Patel, Maria Caulfield and Anne-Marie Trevelyan – wrote a joint article for the ConservativeHome website on Thursday, saying: “Nothing changes the fact that, as the prime minister herself has said, we need to see meaningful, legally-binding changes to the Withdrawal Agreement, removing the backstop.

“We remain open-minded as to how this is achieved, but it must be a treaty-level clause that brings about substantive legal changes. It cannot simply re-emphasise the temporary nature of the backstop, because the attorney general has already said that it could ‘endure indefinitely’.”

One source close to a soft-Brexit minister said there would be “fireworks” either way as next week is the point at which May will have to throw her lot in with either them or the ERG.

The soft-Brexit rebels are particularly buoyed by the idea that the power of the ERG was waning because they would no longer win a no-confidence motion against the prime minister, given that the new Independent Group MPs would be likely to abstain to avoid an election – and their price would be a second referendum.

At the same time as ministers are threatening to resign, May is also facing the possibility of more MPs quitting the party, after Anna Soubry, Sarah Wollaston and Heidi Allen joined the Independent Group citing her Brexit policy and the destruction of the modernising wing of the party. With her working majority down to just eight, May called in two potential defectors – Phillip Lee, a former justice minister, and Justine Greening, the former education secretary – to Downing Street in a bid to persuade them to stay.

The prime minister also wrote back to the defectors saying she “did not accept the picture you paint of our party”, arguing it was still a “moderate, open-hearted Conservative party in the one nation tradition”.

Greening said earlier that she would stay in the party “for the moment”, while Tobias Ellwood, a defence minister, also gave a sympathetic statement about the three defecting Conservatives. “Losing three colleagues raises serious questions about our brand, our core mission and ownership of the very soul of our party which we must address,” he said. “If we have any ambitions of winning support beyond our base we must remain a centre right, inclusive, vibrant and progressive party.”

Dominic Grieve, the former attorney general, is unlikely to quit, but said he would have to leave the party if the government implemented a no-deal Brexit. He told the Guardian “the numbers are there” for May to be defeated on the Cooper-Letwin amendment unless she rules out a no-deal Brexit.

On Wednesday, Philip Hammond repeatedly refused to say whether or not he would resign as chancellor if May decided to pursue a no-deal Brexit.