LONDON — Prime Minister Theresa May of Britain faced a deep political crisis on Thursday after two cabinet ministers quit her government, including Dominic Raab, her chief negotiator on withdrawal from the European Union — decisions that threaten to wreck not only her plans for the exit but also her leadership.
The surprise resignation of Mr. Raab on Thursday morning followed a tense, five-hour meeting of the cabinet the previous day, during which ministers reluctantly agreed to sign off on Mrs. May’s draft plans for departure from the European Union, a process commonly known as Brexit.
Mr. Raab’s departure was not only unexpected but also deeply damaging to Mrs. May’s authority, increasing the risk that she might face a leadership challenge from rebel lawmakers inside her own Conservative Party.
Shortly after his announcement, Esther McVey, the work and pensions secretary, resigned, adding to the turmoil.
The crisis is a grave one for Mrs. May, who addressed lawmakers in Parliament on Thursday morning to sell her deal. Even before the resignations, she most likely knew that she would struggle to gain support from lawmakers for her draft agreement.
“What we agreed yesterday was not the final deal,” she said. “It is a draft treaty that means that we will leave the E.U. in a smooth and orderly way on the 29th of March, 2019, and which sets the framework for a future relationship that delivers in our national interest.”
She added that the deal “delivers in ways that many said could simply not be done.” It would put in place a transitional relationship with the European Union through the end of 2020, while a permanent arrangement is negotiated, but the transition period could be extended.
Jeremy Corbyn, the Labour Party leader, called Mrs. May’s agreement “a leap in the dark, an ill-defined deal by a never-defined date.” The continued uncertainty about Britain’s relationship with Europe, lasting at least another two years and possibly much longer, will accelerate the exodus of businesses and investment that is already underway, he said.
“Parliament cannot, and I believe will not,” accept the arrangement, he added.
That view was echoed by Ian Blackford, a lawmaker from the Scottish National Party, who said the prime minister was “trying to sell us a deal that is already dead in the water.”
Although a hard-line supporter of Brexit, Mr. Raab had been a core member of the cabinet, and his presence had reassured other hard-line lawmakers. He served as Brexit secretary for barely four months, succeeding David Davis, who also resigned, because he felt that Mrs. May was not taking a hard enough line in negotiations.
In his letter of resignation, Mr. Raab said that he could not “reconcile the terms of the proposed deal with the promises we made.”
In the hours after his announcement, the pound dropped 1.5 percent against the dollar.
Ms. McVey’s departure, though damaging, was less of a surprise.
Another cabinet minister, Penny Mordaunt, the international development secretary, was also reportedly reconsidering her position after a cabinet debate on Wednesday that Mrs. May described, diplomatically, as “impassioned.” As many as 10 cabinet ministers were reported to have voiced reservations.
Iain Duncan Smith, a leading Conservative supporter of Brexit and former party leader, told the BBC that the effect of Mr. Raab’s resignation would be “devastating,” because it suggested that the Brexit secretary’s concerns had been ignored, despite his pivotal position in government and in withdrawal negotiations.
Such is the unhappiness from around the party at Mrs. May’s draft deal that the calculation of those who want to oust her might change.
It would take requests from 48 Conservative lawmakers to secure a vote of no confidence in Mrs. May. Though the hard-line pro-Brexit faction has that number, it has held back so far because it does not believe that it has enough support to topple her.
To oust her as prime minister would require a majority of Conservative lawmakers — at least 158 — voting to force her out.
On the floor of Parliament on Thursday, Mrs. May faced a torrent of criticism, much of it from members of her own party. Jacob Rees-Mogg, a leading Conservative Brexit hard-liner, said that the prime minister’s promises and actions “no longer match,” and asked why he should not join those demanding a vote of no confidence.
Another Conservative lawmaker, Julian Lewis, described her deal with Europe as “a ‘Hotel California’ ’’ Brexit deal which ensures that we can never truly leave the E.U.”
Britons voted to quit the European Union in a 2016 referendum, but since then the Conservatives have been split between those who want to keep some close economic ties to the bloc, to protect the economy, and others who want a cleaner break.
Worryingly for Mrs. May, many of her enemies, on both the right and the left, are converging around the view that the compromise she has carefully forged is the worst of both worlds, leaving Britain without a voice in the European Union but still subject to many of its trade rules. Several leading Brexit supporters have characterized the draft deal as worse than membership in the bloc they find so objectionable.
The focus of the discord has been around plans to ensure that, whatever happens in future trade talks, there should be no physical checks at the border between Northern Ireland, which is part of the United Kingdom, and Ireland, which is a member of the European Union.
Under the so-called backstop plan that is part of the draft deal, the whole of the United Kingdom would remain in a customs union with the European Union until future trade plans that negate the need for border checks are worked out.
But Northern Ireland would be subject to more of the European Union’s regulatory processes than the rest of the country, a fact that Mr. Raab said “presents a very real threat to the integrity of the United Kingdom.”
He also objected to the fact that Britain could not unilaterally leave the backstop, a move that would clear a path to exit a customs union and pursue trade deals with other countries.
One of Mr. Raab’s under-secretaries for Brexit, Suella Braverman, also stepped down on Thursday. Their departure had been preceded on Thursday morning by the resignation of Shailesh Vara, a junior Northern Ireland minister.
Speaking at a news conference in Brussels shortly before Mr. Raab’s announcement, Michel Barnier, the top European Union negotiator, and Donald Tusk, the president of the European Council, said they would call a summit meeting for Nov. 25, where leaders of the bloc’s member states could endorse the deal.
Mr. Tusk said that the accord approved by the British cabinet meets two crucial objectives: It limits the damage Brexit would cause, and it protects the vital interests of the 27 remaining members states and the European Union as a whole.
“We have always said Brexit is a lose-lose situation and these negotiations were always about damage control,” he said.
Mr. Barnier said that the coming days, when the focus will be on finalizing a political declaration outlining the future relationship between Britain and the European Union, would be “intense,” adding that “we have no time to lose.” Brexit is scheduled to take effect on March 29.
However, European Union officials have made it clear that they were scheduling the summit meeting on the assumption that turbulence in Mrs. May’s party would not paralyze or overwhelm her government.