Theresa May is being warned by her team that she cannot sack ministers who vote this week to delay Brexit without causing a further rupture within her party.

Close allies of the prime minister have concluded that so many government members are planning to back an amendment that could delay Brexit that firing them all is not a realistic option. Instead, she is being urged to either head off the row by promising a binding vote on delaying Brexit next month, or give way and allow her ministers permission to vote for the measure on Wednesday.

‘Delaying Brexit may be our last chance to prevent a historic mistake’ Read more

It comes after three Tory MPs resigned from the party last week, partly in protest at May’s handling of Brexit, while a trio of cabinet ministers took the highly unusual step of publicly signalling they could vote to delay withdrawal from the EU.

Lord Heseltine, the former Tory deputy prime minister, warned more resignations would happen unless MPs were allowed to tackle the “most catastrophic aspect of Brexit” and block a no-deal outcome. “Certainly my advice would be to those who have doubts, stay and fight,” he said. “Don’t acquiesce. I would hope that the Conservatives that I know will take a no-deal off the table.”

Amber Rudd, David Gauke and Greg Clark jointly wrote a newspaper article warning that they would join MPs pushing for an extension to article 50 if there is no significant progress this week. Senior Tories believe that the resignations of Anna Soubry, Heidi Allen and Sarah Wollaston have made it too dangerous to sack ministers willing to vote for a Brexit delay.

MPs are due to vote on the contentious plan to delay Brexit – proposed by Oliver Letwin, the former Tory cabinet minister, and Labour’s Yvette Cooper, the chair of the home affairs select committee – on Wednesday. It would oblige the government to ask for a delay if a deal has not been sealed by the middle of March. Britain is due to leave the EU at the end of next month.

In an article for the Observer, Letwin states that a vote for his plan would open the door to parliament taking control of the Brexit process. “If we don’t act now, the UK will sleepwalk out of the EU in just over 30 days with no deal whatsoever,” he writes. “Many of us on the Conservative benches have already voted for the prime minister’s deal once. We are more than prepared to do so again next week and in coming weeks. But we have watched with increasing dismay as the government has shuffled, bit by bit, towards a cliff edge.

“The prospect of falling by mistake into a no-deal Brexit, simply because we have failed to create an opportunity for cross-party consensus to emerge, would be a tragic and historic mistake.”

However, there are also huge dangers for No 10 in allowing ministers to back the move. One cabinet minister said such a decision would “look like the government failing to take responsibility for delivering Brexit on time”, and cause a revolt among Tory Brexiters.

In a sign of growing grassroots pressure on MPs, Tory activists gathering for the party’s national convention on Saturday passed a motion opposing any attempt to delay Britain’s EU exit. “The national convention supports the commitments the prime minister has made to the country to honour the European Union referendum result of 2016 so that having triggered article 50 we will leave the European Union on 29 March 2019,” it states.

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“Another referendum, a delay beyond the European elections, taking no-deal off the table or not leaving at all would betray the 2016 people’s vote and damage democracy and our party for a generation.”

In an attempt to calm divisions, the prime minister told the convention that the Tories were not “a party of purges and retribution” and called for an end of attempts to deselect MPs over Brexit.

“While I know it hurts to lose a fellow Conservative, our reaction has been the right one,” she said. “To listen to their reasons, even if we disagree with them. To explain politely where we think they’re wrong. To respect the sincerity of their decision, even if we regret it.”

She also told her audience that she would not allow the referendum vote to leave the EU to be frustrated. “Our focus to deliver Brexit must be absolute,” she told the behind-closed-doors meeting, according to extracts released by No 10.

“We must not, and I will not, frustrate what was the largest democratic exercise in this country’s history. In the very final stages of this process, the worst thing we could do is lose our focus.”

May will be at an EU-Middle East summit on Sunday to hold talks with figures including the European council president, Donald Tusk, and Germany’s chancellor, Angela Merkel, as she battles to secure a revised deal acceptable to the right of her party.