A Tory MP who has put forward a plan to block a no-deal Brexit says ministers have told him they will quit, if they are ordered to vote against it.
His cross-party bill would force Theresa May to request an extension of Article 50 if she can’t get a deal approved by MPs by the end of February.
Mr Boles told the BBC his bill had a “broad base” of support from different sides of the Brexit debate.
And he said he believed a number of ministers backed his plan.
Theresa May has been meeting senior members of other parties to see if there is any room for a compromise after her EU withdrawal deal was overwhelmingly rejected by MPs this week. Labour Leader Jeremy Corbyn has refused to attend talks until the prospect of a no-deal Brexit has been ruled out.
The prime minister will publish a new plan on Monday with a full debate and key vote scheduled for Tuesday, 29 January.
Mr Boles’s EU Withdrawal (Number 2) Bill aims to put Parliament in control of the Brexit process, demanding an extension to the Article 50 process to allow negotiations to continue beyond the scheduled date of Brexit on March 29.
But Mr Boles withdrew proposals for the cross-party Commons Liaison Committee of senior backbenchers to draw up an alternative Brexit plan, after its chair Sarah Wollaston indicated that it would not accept the role.
However the Tory backbencher told Nick Robinson’s Political Thinking podcast the bill would still go ahead and had sponsors from three different parties – the Conservatives, Labour and the Lib Dems.
“This bill is about creating the space for a compromise by ruling out a no-deal Brexit,” he told the BBC.
To pass his new bill, Mr Boles will need to suspend the rules in Parliament so that he does not need government support to free up parliamentary time for it.
He could do this by amending the government’s business motion which sets out the schedule ahead of the Commons debate on 29 January.
He told the Political Thinking podcast: “We have had indications that many ministers, including cabinet ministers are very, very keen to see it pass and are telling the prime minister that they will not vote against it.
“There is a bandwagon rolling, it’s got a lot of momentum behind it and I very much hope that any MP who shares my view that a no-deal Brexit would be a disaster, will jump on board.
“I have been told directly by ministers, not in the cabinet, that they have said that they would resign if they are whipped to vote against it.”
While he did not know if any cabinet ministers would quit, he said the transcript reported in the Daily Telegraph of a conversation in which Philip Hammond “made quite plain that he thought this was fantastic”.