The work and pensions secretary, Esther McVey, has become the second senior minister to quit the cabinet, following the Brexit secretary, Dominic Raab, out of the door and throwing Theresa May’s government into turmoil.

McVey, an arch Brexiter who was known to be unhappy with the prime minister’s Brexit plans, said they had failed to “honour the result” of the referendum and had crossed her own red lines for leaving the EU.

During a tense five-hour cabinet meeting on Wednesday, McVey twice called for a vote to be taken on the deal. In her resignation letter to May, she wrote: “We have gone from no deal is better than a bad deal, to any deal is better than no deal.”

Her departure came after Raab resigned as Brexit secretary saying he “cannot in good conscience” support the deal agreed by the cabinet, kicking off what was expected to be a day of turmoil for the prime minister as she struggles to retain control of her party.

One of Raab’s junior ministers, Suella Braverman, a former chair of the hardline Brexit ERG group of Tory backbenchers, also quit, saying that the public would see the plans as “a betrayal”.

Downing Street insiders are keeping a particularly close eye on the international development secretary, Penny Mordaunt, who has also publicly voiced reservations in recent days. The Commons leader, Andrea Leadsom, has also talked of serious concerns and warned May she will struggle to get her plans through the Commons.

As the beleaguered prime minister prepared to give a statement to MPs, she also faced the threat of a no confidence vote from her own backbenchers amid rumours that the critical threshold of 48 MPs had been reached.

The departure of Raab, seen as a crucial figure in May’s attempts to sell her proposed deal to other Brexit-minded Tory MPs, follows the resignation earlier on Thursday of the junior Northern Ireland minister, Shailesh Vara.

In his resignation letter Raab said the proposed arrangement to avoid a border with Northern Ireland through a backstop arrangement is a “very real threat to the integrity of the United Kingdom”.

He added: “I cannot support an indefinite backstop arrangement where the EU holds a veto over our ability to exit.”

He claimed the arrangement negotiated with the EU’s Michel Barnier, amounted to a “hybrid of the EU customs union and single market obligations”.

Raab wrote: “No democratic nation has ever signed up to be bound by such an extensive regime, imposed externally without any democratic control over the laws to be applied, nor the ability to exit the arrangement.”

There will be concerns at No 10 that Raab and McVey’s departures could be the first two of a number of cabinet resignations, after Wednesday’s stormy five-hour meeting, during which a string of senior ministers raise objections to May’s Brexit deal.

In her letter, McVey cited concerns over the future of the EU and a lack of control over money, law, borders and trade policy under May’s Brexit deal which she felt kept the UK too close to Brussels.

“The British people have always been ahead of politicians on this issue, and it will be no good trying to pretend to them that this deal honours the result of the referendum when it is obvious to everyone that it doesn’t,” she wrote.

“We have gone from no deal is better than a bad deal, to any deal is better than no deal. I cannot defend this, and I cannot vote for this deal. I could not look my constituents in the eye were I to do that. I therefore have no alternative but to resign from the government.”

The Brexit secretary’s departure came an hour-and-a-half before Theresa May was due in the Commons to sell her EU divorce deal to largely sceptical MPs. McVey’s just half an hour before.

Raab had been at the heart of the Brexit negotiations, and he was the first minister that May discussed the final deal with on Tuesday lunchtime, where it had been agreed that the text achieved was the best available and should be put to cabinet.

A string of hard Brexit Conservatives, who will be emboldened by Raab’s departure, have voiced concerns about the plan and have said they will vote it down when it comes before MPs for ratification next month.

Today, I have resigned as Brexit Secretary. I cannot in good conscience support the terms proposed for our deal with the EU. Here is my letter to the PM explaining my reasons, and my enduring respect for her. pic.twitter.com/tf5CUZnnUz — Dominic Raab (@DominicRaab) November 15, 2018

Raab’s letter ended: “Above all, I cannot reconcile the terms of the proposed deal with the promises we made to the country in our manifesto at the last election. This is, at its heart, a matter of public trust.

“I appreciate that you disagree with my judgment on these issues. I have weighed very carefully the alternative courses of action which the government could take, on which I have previously advised. Ultimately, you deserve a Brexit secretary who can make the case for the deal you are pursuing with conviction. I am only sorry, in good conscience, that I cannot.”

Anna Soubry, the remain-backing Tory MP, tweeted: “Raab’s resignation marks the end of PM’s withdrawal agreement. This is v serious, the PM will clearly be considering her position.”

Jon Trickett, Labour’s shadow Cabinet Office minister, said: “The government is falling apart before our eyes as for a second time the Brexit secretary has refused to back the prime minister’s Brexit plan. This so-called deal has unravelled before our eyes.”

Raab is the second Brexit secretary May has lost in a matter of months – Raab took over the job after David Davis resigned in July in protest at May’s course of action. At that time Boris Johnson also resigned as foreign secretary.