Theresa May faces a critical 24 hours after her Brexit secretary sensationally quit over the plans for how the UK will leave the European Union.

David Davis’ decision to resign from the cabinet has left the government in chaos. The question now is “will any more of the cabinet follow him out of the door?”

All eyes will now turn to foreign secretary Boris Johnson whose aides have been briefing his disappointment over the Brexit plan laid out by the prime minister at her country retreat Chequers last Friday.

And there is certainly enough disgruntled backbench MPs who are willing to write to the 1922 committee chairman Sir Graham Brady to force a leadership challenge.

But that alone would not solve the Brexiteers’ problems. If there is a challenge and, as would be expected, Mrs May stood for re-election as leader she probably has the numbers to win. This would give her a clear mandate to continue with her Brexit plan.

Mr Davis has ruled himself out of the running if there was to be a contest. But there are other big beasts in the cabinet who would worry Number 10, namely Mr Johnson and environment secretary Michael Gove.

Mr Gove, who led the Leave campaign alongside Mr Johnson, has given his backing to the agreed plans but there is little doubt he will have been disappointed by great swathes of the proposal.

Mrs May moved quickly to appoint the staunchly anti-EU Dominic Raab as the new Brexit secretary – a shrewd move that should calm some Brexiteer nerves.

Speaking on Radio 4’s Today programme, Mr Davis said: “In my view, this policy has got a number of weaknesses.

“I would be front and centre in delivering this policy, explaining it to the House, persuading the House it is right, and then going out and delivering it with the EU.

“Frankly, just as it was known what the policy was, it was also known I had concerns about it.

“It would not have been a plausible thing to do and I wouldn’t have done a good job at it.”

Jacob-Rees Mogg, who leads the powerful Eurosceptic faction of Tory MPs the European Research Group, said he believed a vote of no confidence would probably not happen immediately but added: “I think what the prime minister needs to do is give up on the Chequers proposals which, David Davis has pointed out in his resignation letter, don’t actually deliver Brexit.”

To trigger a no-confidence vote, 15% of Tory MPs must write to Sir Graham. With 316 Conservative MPs in the House of Commons, Sir Graham must receive 48 letters to call a ballot.

If Mrs May chose to fight, she would need the support of more than 50% of Conservative MPs – currently 159 – in the confidence vote to stay in office.

But even if she achieved that threshold, a narrow victory would seriously undermine her authority and may lead her to question whether it was worth carrying on.

If she lost the vote, she would not be able to stand in the subsequent leadership contest, arranged by Sir Graham.

Candidates for the leadership must be nominated by two Conservative MPs. If only one candidate comes forward, he or she becomes leader.

If a number of would-be leaders are nominated, the list is whittled down to a shortlist of two by MPs before being put to party members in the country.

In a series of secret ballots taking place within a few days at Westminster, MPs vote for their preferred leader, with the least popular candidate eliminated after each round until only two remain.

The final two then go to a postal ballot of all party members, with the position of leader, and in this instance prime minister, going to the victor.

Sir Graham would be responsible for overseeing the contest and setting a timetable for the campaign, which would be expected to last around 12 weeks. This timescale would worry both Brexiteers and Remainers with key EU deadlines looming in the autumn.

One East Anglian MP, speaking off the record, said: “I am not entirely surprised as he is a bit of a maverick, and if cabinet-level resignations are limited to DD then I think the prime minister will probably survive. If not then who knows ...”