Matt Hancock insisted this morning any customs backstop would be “time limited” – but at the same time would not say whether a date at which it expired would be written into the deal.

The health secretary’s appearance on the Andrew Marr came as Theresa May faces Cabinet resignations and increased pressure from her DUP allies over Brexit as a key summit with EU leaders looms.

Former Brexit secretary David Davis said today the prime minister’s plan was “completely unacceptable” and urged Cabinet ministers to “exert their collective authority”.

Andrea Leadsom, Penny Mordaunt and Esther McVey are among the Cabinet ministers reportedly considering their positions.

DUP leader Arlene Foster is said to have concluded that a no-deal Brexit was now the most likely outcome after talks with senior figures including Michel Barnier in Brussels.

The issue of the border between Northern Ireland and Ireland is one of the last remaining obstacles to achieving a divorce deal, with wrangling continuing over the nature of a “backstop” to keep the frontier open if a wider UK-EU trade arrangement cannot resolve it.

The EU version, which would see just Northern Ireland remain aligned with Brussels’ rules, has been called unacceptable by May and is loathed by the DUP.

May’s counter-proposal is for a “temporary customs arrangement” for the whole UK, but Tory Brexiteers are suspicious this could turn into a permanent situation, restricting the freedom to strike trade deals around the world.

Speaking to Marr this morning, Hancock said the proposal was “that it will be temporary and time limited”

But asked if there would be a date, he said: “There are different ways to ensure that something is time limited.”

He suggested there could be conditions for “the point at the which arrangements come to an end”.

And asked if there would be a “break” clause, Hancock added: “There are different ways that you can make sure that something is credibly time limited and that’s what I want to see.”

Hancock told Cabinet colleagues there was “no reason” resign although he added that he “didn’t expect” David Davis and Boris Johnson to quit after Chequers.

Tory vice chairman James Cleverly told Sky News’ Sophy Ridge on Sunday that Cabinet ministers should use their position to influence Brexit policy rather than resign.

“They should use that position to put their ideas forward, I would suggest that’s a much more constructive and helpful way of influencing the direction of the negotiations with the EU,” he said.

But Iain Duncan Smith said Cabinet ministers who did not agree with the prime minister’s Brexit deal should quit.

“I share one thing in common with David Davis which is we both resigned from the Cabinet when we weren’t in agreement with it and therefore I am always of the view that when you get to the point where you are no longer agree on a fundamental issue, then it’s probably time that you found yourself on the back benches,” he said.

“I don’t want to see a leadership change, I want to see a leadership change her mind and go in a different direction”

Emily Thornberry, the shadow foreign secretary, repeated that Labour would not vote for a “just a fudge” deal “cooked up” between May and Brussels.

She rejected the suggestion Labour’s six tests for whether it would back a deal were “silly”.

“We’re not voting for something that’s essentially a bridge to nowhere,” she told Marr.

And she attacked the “ridiculous binary choice” on Brexit being offered.

“I think it’s false,” she said. “We said we wanted a meaningful vote and we can’t see why we should have, on the one hand Theresa May’s nonsense and on the other hand a no deal, because that’s what they’re threatening us with.

Downing Street might have to rely on Labour MPs defying orders to vote against the Brexit deal in order to win the vote in the Commons.

Caroline Flint this morning told Ridge on Sunday that she might side with the prime minister

“I think if a deal like that comes back it cannot be called a hard Brexit and I would have to very much weigh up what my decision is and, to be honest, if it’s a reasonable deal that meets all those requirements that I’ve put forward to support a deal, then I think I would,” she said.

Crunch time will come on Tuesday when the Cabinet meets and is asked to approve May’s proposal.