British Prime Minister Theresa May, right, sits with cabinet adviser David Davis and British Foreign Secretary Boris Johnson inside 10 Downing Street in London on Nov. 28, 2016. (Peter Nicholls/AFP/Getty Images)

EVER SINCE Britain voted to leave the European Union two years ago, the exit has been complicated by the refusal of its chief promoters to face the fundamental contradictions in their position. They claimed that the country could escape from the diktats of the E.U. bureaucracy in Brussels and the European Court of Justice and curtail the flow of European workers across British borders without wrecking the economy, which is heavily dependent on free trade with Europe. In fact, it has long been clear that the government of Theresa May must choose between losing privileged access to continental markets — on which both large manufacturing industries and the crucial London financial sector depend — and accepting continued E.U. regulation in some form.

After prolonged and damaging procrastination, caused by deep divisions in her Conservative Party, Ms. May finally bowed to reality last week. She presented her cabinet with a plan for a “soft” Brexit that would, among other things, accept E.U. rules for manufacturing and agriculture. The program, which has yet to be disclosed in full, might not pass muster with E.U. leaders, who have been reluctant to grant Britain any special arrangements as it leaves the bloc. But with time running out to complete negotiations before the Brexit date next March, it was, at least, an important step in the right direction.

This week came the consequence: Two of the most aggressive and irresponsible promoters of Brexit — Foreign Secretary Boris Johnson and Brexit negotiator David Davis — resigned from Ms. May’s cabinet. The resulting political crisis threatens to topple Ms. May from office and perhaps even trigger a general election. But if the prime minister can survive — which was looking more likely than not by Tuesday — she will have successfully passed a hurdle she should have tackled long ago.

Mr. Johnson and Mr. Davis, who campaigned hard for Brexit, have never offered their own plan for how it might work — though Mr. Johnson recently mused that President Trump’s tactics of provocation and bluster should have been employed. Meanwhile, the Brexit hard-liners have been quick to offer theatrical denunciations of any steps by Ms. May toward solving such problems as how to retain British-based automotive and aviation firms dependent on European markets and supply chains, and how to keep the open border between Northern Ireland and the Republic of Ireland. By continuing to accept some E.U. standards, “we are truly headed for the status of colony,” Mr. Johnson thundered in his resignation letter.

Mr. Johnson imagines a world in which Britain would be a fiercely sovereign island, as it was in the 19th century. Acting on that ideology would likely lead the country to crash out of the E.U. next year and trigger a crisis that would cost tens of thousands of jobs while creating administrative chaos. Slowly and painfully, Ms. May is attempting to structure a compromise that would retain Britain’s place in the interdependent global economy of the 21st century and its place of influence in international affairs while returning some authorities from Brussels to London.

The United States, which has a strong interest in continued British prosperity and clout, ought to be encouraging such a deal. Instead, Mr. Trump, who is due to visit London this week, predictably appears inclined to back Mr. Johnson, because “he’s been very, very nice to me.” Someone should tell the president that his friend is looking like a loser — and is best avoided.