LONDON — For Prime Minister , this was supposed to be a critical week to reset his government after a tumultuous round of infighting that led to the abrupt ouster of his most influential adviser, Dominic Cummings.

Instead, Mr. Johnson began a 14-day quarantine in his Downing Street residence on Monday after being exposed to a member of Parliament who tested positive for the coronavirus.

The prime minister insisted he was “fit as a butcher’s dog” and was merely heeding the rules of Britain’s test-and-trace program. But Mr. Johnson’s enforced isolation will hobble his plan to regain momentum with public appearances and policy announcements after days of corrosive palace intrigue among his closest advisers.

The prime minister’s second close call with the virus — last April, he was hospitalized with a severe case of — deepens the sense of a government that cannot seem to get out of its own way.

The latest upheaval also comes at a pivotal moment in the negotiations for a post-Brexit trade agreement between Britain and the European Union. With the clock running down and major issues still dividing the two sides, Mr. Johnson will have to make difficult compromises in the next two weeks to break the deadlock.

The departure of Mr. Cummings removes an influential Brexiteer from the equation, but it also makes it harder for Mr. Johnson to cut a deal with Brussels without being accused of an instant Brexit betrayal.

ImageInstead of Regaining Momentum, Johnson Is Stalled at Home Again
Credit…Henry Nicholls/Reuters

Mr. Johnson’s exposure to the virus this time came during a meeting with Conservative lawmakers, one of whom, Lee Anderson, later developed symptoms and tested positive. A photo showed the two men standing barely three feet apart — neither wearing a mask — which raised questions about whether Downing Street practices proper social distancing, even after the outbreak that infected Mr. Johnson in March.

“The good news is that N.H.S. test-and-trace is working ever more efficiently,” Mr. Johnson said in a video in which he tried to promote the National Health Service’s much-maligned program. “The bad news is they pinged me and I’ve got to self-isolate because somebody I was in contact with a few days ago has developed Covid.”

As a recovered patient, Mr. Johnson said his body was “bursting with antibodies.” He did not broach the risk of re-infection, which, while possible, is rare. Mr. Johnson’s well-worn description of himself as “fit as a butcher’s dog” refers to a robust creature, well-fed on scraps from his master’s cutting board.

The same cannot be said for Mr. Johnson’s government, according to critics. The sudden loss of Mr. Cummings will deprive the prime minister of his most prodigious font of ideas and projects, even if critics also faulted the adviser for being a toxic, unyielding presence in Downing Street, clashing with other officials and straining Mr. Johnson’s ties with members of his party in Parliament.

The infighting cast an unwelcome spotlight on Mr. Johnson’s fiancée, Carrie Symonds, who previously worked as communications director for the Conservative Party. Ms. Symonds reportedly raised objections to the elevation of an ally of Mr. Cummings’s, Lee Cain. When that blocked Mr. Cain’s path, it set off a confrontation that resulted in the departure of both him and Mr. Cummings.

With a new lineup of advisers, Mr. Johnson’s allies hope he will recapture the more likable, easygoing image he enjoyed when he served as mayor of London.

This week, he plans to roll out a climate initiative and redouble his commitment to “level up” Britain’s economically challenged north with the more prosperous south. That is vital to Mr. Johnson’s political fortunes since the Conservatives won a landslide majority by breaking the Labour Party’s so-called “red wall” in those regions.

Mr. Anderson, the Conservative lawmaker who tested positive, is precisely the kind of figure to whom Mr. Johnson hopes to reach out. A onetime coal miner and Labour Party functionary in the district of Ashfield, Mr. Anderson, 53, ran as a Conservative in the last election and won a seat long held by Labour.

Credit…John Sibley/Reuters

“It’s like the country is turning upside down,” Mr. Anderson said last year when he was canvassing voters. “As bizarre as it seems, Boris and Donald Trump connect with working-class voters. People like plain English.”

Mr. Anderson, on his Facebook page, said he lost his sense of taste on Friday, a day after he and four other lawmakers attended a breakfast meeting with Mr. Johnson. His positive test was returned on Sunday, which prompted the National Health Service’s contact tracers to get in touch with Mr. Johnson.

During his self-isolation Mr. Johnson plans to work from his apartment, which is above 11 Downing Street. He will also have access to his office at number 10 next door without walking through parts of the building where others work. Unlike his previous period in quarantine, Mr. Johnson will not have to live apart from his family.

Mr. Johnson will maintain a full schedule of events, conducted remotely, and hopes to use a video link to take part in Prime Minister’s Questions, his weekly grilling by the leader of the opposition in the House of Commons.

Although this is yet another critical week for the trade negotiations, analysts expect a meeting of European Union leaders on Thursday to be another in a succession of missed deadlines. Unlike many such negotiations, which come down to obscure details, this one has reached a politically charged endgame, with disputes over fishing rights, state aid rules, and guarantees of fair-market competition.

“It’s not insoluble, but we are in a holding pattern,” said David Henig, director of the U.K. Trade Policy Project at the European Center for International Political Economy, a research institute. “The political issues haven’t been resolved, and nothing is being done differently that makes one think that they can.”

“Some of these problems should have been solved and there should be narratives taking us toward a deal,” Mr. Henig added. “So the question is: What is going to change now that is going to make it happen?”

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