LONDON — Prime Minister Theresa May was trying on Monday to save her strategy for quitting the European Union after the late-night resignation of her chief negotiator for withdrawal, David Davis, who stepped down in protest over her plans for Brexit, Britain’s departure from the bloc.
Mrs. May’s proposal, which would keep close economic ties to the bloc, won agreement after a day of negotiations by a divided cabinet on Friday. Mr. Davis’s resignation Sunday night revealed the intensity of the split within the cabinet.
Mr. Davis was among the members of the prime minister’s cabinet demanding a cleaner break from the European Union, known as a “hard Brexit,” and his decision to step down raises questions about whether others who share his view, like the foreign secretary, Boris Johnson, will stay in their posts.
Mr. Davis said in a statement released late Sunday that he could not accept the approach that Mrs. May demanded in the meeting with top officials on Friday.
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 his letter. “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, who will address Parliament on Monday, disputed Mr. Davis’s assessment of the situation, saying that whatever deal is reached will “undoubtedly mean the returning of powers from Brussels to the United Kingdom.”
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-line 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 not reject the European demand for free movement of people across borders, although goods would be allowed to pass between Ireland (which is part of the bloc) and Northern Ireland (which will not be).