LONDON — Prime Minister Theresa May of Britain was battling to save her government on Monday after her foreign secretary quit over Brexit, deepening a mood of crisis just eight months before the country is due to leave the European Union.
The foreign secretary, Boris Johnson, was the second minister to leave her cabinet within 24 hours, as Mrs. May pushed ahead with a proposal that would keep Britain more closely tied to the European Union than hard-line conservatives want.
Just last week, she appeared to have won the full cabinet’s agreement on keeping Britain’s economy closely anchored to the European Union. But the resignations reopened speculation about a challenge to her leadership, something that Mrs. May’s official spokesman said she would fight.
But with the Brexiteers in the party in full revolt, Conservative insiders predicted further resignations unless and until Mrs. May drops her plan.
The turmoil comes days before a scheduled visit by President Trump, a champion of the kind of sharp break with the European Union that Mrs. May has deemed unworkable. She is nevertheless expected to seek assurances from Mr. Trump that the United States is ready to enter negotiations on a bilateral trade agreement.
Yet, in recent weeks, several major British employers have issued warnings over the risks of Brexit. Most prominently, Jaguar Land Rover said that a chaotic Brexit deal would threaten to derail more than $100 billion worth of investment plans in Britain and force the closure of some factories. Airbus and BMW also questioned whether they could continue to keep manufacturing facilities in the country under those conditions.
The public face of the 2016 campaign that persuaded Britons to quit the European Union, known as Brexit, Mr. Johnson is perhaps the most high-profile advocate of leaving the bloc.
On several occasions, Mr. Johnson had appeared to undermine Mrs. May’s strategy, and in comments that were recently leaked, he described her government as lacking “guts,” unfavorably comparing the prime minister’s negotiating style to that of President Trump.
After the surprise resignation of David Davis, Britain’s chief negotiator in withdrawal talks with the European Union, there was an ominous silence Monday morning from Mr. Johnson, who was scheduled to host a diplomatic meeting in London to discuss the western Balkans.
Then, around 3 p.m., Mrs. May’s office issued a statement that said simply: “This afternoon, the prime minister accepted the resignation of Boris Johnson as foreign secretary. His replacement will be announced shortly. The prime minister thanks Boris for his work.”
The pound dropped against the dollar as news of the resignation broke, and Conservative lawmakers appealed to their colleagues not to demand a confidence vote in Mrs. May’s leadership.
Such a move could be set off by 48 of her party’s lawmakers — although it would take many more to dislodge her. Earlier, Mr. Davis told the BBC that he was not encouraging a challenge to Mrs. May, and ruled himself out as a contender if there were one.
But the resignation of Mr. Johnson renewed the debate just as Mrs. May was hoping that she had restored some stability to the government by announcing that the pro-Brexit lawmaker Dominic Raab would replace Mr. Davis.
Addressing Parliament on Monday, Mrs. May said the options presented so far by European Union negotiators were unacceptable to Britain.
“If the E.U. continues on this course, there is a serious risk it could lead to no deal, and this would most likely be a disorderly no deal,” she said. “A responsible government must prepare for a range of potential outcomes.”
As a result, she said, the cabinet agreed on Friday to step up preparations for such an outcome, although she acknowledged that a sudden, hard exit without any agreements on trade, customs or migration “would have profound consequences for both the U.K. and the E.U.,” and should be avoided.
The resignation of Mr. Davis, who was among the members of the prime minister’s cabinet demanding a more complete break from the European Union, a so-called a hard Brexit, revealed the intensity of the split in the cabinet, although he did not appeal to other ministers to follow him.
Mr. Davis said that he could not accept the approach that Mrs. May demanded in the meeting with top officials on Friday, contending that Britain was giving away too much, too easily in negotiations with Brussels, and that he was leaving his job because he could not, in conscience, argue for the cabinet’s Brexit position in public.
Other members of Mrs. May’s cabinet have been arguing for a “soft Brexit,” which would seek to maintain economic stability by keeping closer ties to the European Union after Britain leaves.
Mr. Davis specifically cited concerns about any agreement that would leave Britain in a customs union and the single market.
“The general direction of policy will leave us in, at best, a weak negotiating position, and possibly an inescapable one,” he wrote in a letter to the prime minister that was released publicly. “The cabinet decision on Friday crystallized this problem.”
Mr. Davis acknowledged that there were no guarantees of what would happen after Britain leaves the bloc, but he said that Mrs. May’s strategy meant that his position as chief negotiator was untenable.
“This is a complex area of judgment, and it is possible that you are right and I am wrong,” he wrote. “However, even in that event, it seems to me that the national interest requires a secretary of state in my department that is an enthusiastic believer in your approach, and not merely a reluctant conscript.”
Mrs. May disputed Mr. Davis’s assessment of the situation, saying that whatever deal is reached would “undoubtedly mean the returning of powers from Brussels to the United Kingdom.”
Speaking to the BBC on Monday, however, Mr. Davis, said the prime minister’s plan to return power to the British Parliament was “illusory rather than real.”
Mr. Davis’s announcement prompted an additional departure: Steve Baker, a prominent advocate of a British withdrawal who served as an under secretary in the Department for Exiting the European Union, will leave his post, the BBC reported.
Britain faces a deadline of March 29, 2019, to reach a deal with the European Union. Progress has been slow and difficult, but Mrs. May appeared to have taken a big step on Friday in the meeting with her cabinet at Chequers, the prime minister’s country estate, by bringing advocates of a hard Brexit into line.
The government released a declaration after the meeting that the cabinet would seek “a common rule book for industrial goods and agricultural products,” meaning that — pending an agreement with the European Union — it would continue to abide by the bloc’s rules in that area, although it would no longer have any say over how those rules are shaped and approved.
At the same time, the government would no longer be bound by European rules for services, an approach intended to give Britain more freedom in banking and finance, which represent a huge part of the Britain economy.
The plan announced on Friday also means that Britain would reject the European demand for free movement of people across borders, although goods would be allowed to pass freely between Ireland (which is part of the bloc) and Northern Ireland (which will not be).
While Mrs. May’s cabinet agreed on its negotiating stance, it was not clear which of its positions — if any — the European Union would accept.
“Politicians come and go, but the problems they have created for people remain,” Donald Tusk, the president of the European Council, wrote on Twitter, shortly after Mr. Johnson’s announcement. “I can only regret that the idea of #Brexit has not left with Davis and Johnson. But…who knows?”
Follow Stephen Castle on Twitter: @_StephenCastle
Michael Wolgelenter and Richard Pérez-Peña contributed reporting.