And a suggestion by the chancellor of the Exchequer, Philip Hammond, that the outcome of Brexit might be to move the British and European economies only “very modestly, apart” provoked calls from Brexit supporters for him to be fired.

Not that the pro-Europeans are content with Mrs. May either.

Debate starts Tuesday in the House of Lords, the unelected second chamber of Parliament, on her Brexit legislation. Her critics hope to pass as many as 10 amendments, including one that would scrap plans to enshrine next March’s withdrawal date in law, making it easier to postpone Brexit if negotiations break down.

Mrs. May’s recent reshuffle of her cabinet has inadvertently sharpened debate among pro-Brexit right-wingers by promoting some right-wingers into the government, and freeing up the leadership of the European Research Group, a collection of pro-Brexit Conservative lawmakers.

That allowed Mr. Rees-Mogg to become its new leader, giving an influential platform to the quirky, cartoonish, right-winger who has emerged as a surprise potential candidate to take over from Mrs. May.

Perhaps in response to that competition, the leading Brexit right-winger in the cabinet, Boris Johnson, the foreign secretary, has raised his profile, straying well beyond his brief to suggest more funding for the health service, then making headlines by calling for the construction of a bridge across the English Channel.

While would-be successors to Mrs. May, like Mr. Johnson, are limbering up, it is not clear that a contest is imminent. There is no agreed candidate to take over from Mrs. May and both pro- and anti-Europeans worry they might get someone worse.