Ms. Symonds was not by Mr. Johnson’s side when he addressed the Conservative Party as its new leader on Tuesday. (“Where’s Carrie Symonds?” The Mirror asked.)

Asked about the argument at a televised campaign event last month, Mr. Johnson repeatedly danced around the question. “I think what people have come here today, seductive interviewer though you are, I think people have, I don’t think they want to hear about that kind of thing,” he said.

Mr. Johnson and Ms. Wheeler have four children together. Mr. Johnson, whose womanizing has been the subject of extensive coverage in the British news media, is the father of at least one child from an extramarital affair. He and Ms. Wheeler had split up several times before but had always gotten back together.

Their marriage has now broken up for good, friends say, over his relationship with Ms. Symonds.

Ms. Symonds was spotted with her mother over the weekend moving things into a new house in Camberwell that, according to newspaper reports, she and Mr. Johnson have bought together.

The Brexit-supporting Daily Telegraph, a kind of in-house organ for Mr. Johnson that tends to know what is going on with him, reported a few days ago that Ms. Symonds does plan to move into 10 Downing Street. But she will do it quietly and over the coming weekend, the paper claimed, so as not to draw attention to herself during what she feels is meant to be “Boris’s moment.”

A spokesman for Mr. Johnson did not return an email seeking comment.

In the 2003 film “Love Actually,” a single prime minister (Hugh Grant) starts dating a young woman (Martine McCutcheon) who brings tea to his office every afternoon. But there is little precedent in real life for a First Partner in Downing Street, and it is unclear what, if any, formal role Ms. Symonds would have in Mr. Johnson’s premiership.

The new prime minister — who has an air of personal disorganization, tends to lose things, and used to lug his belongings to and from work in a backpack slung over his shoulders — is said to have lived with friends, and at his house in Thame, Oxfordshire, over the past few weeks.

He and Ms. Wheeler have reportedly sold their family home in Islington, London. Since their argument, neither Ms. Symonds nor Mr. Johnson appear to have stayed in her apartment.

But the job of prime minister comes with government-sponsored housing at 10 Downing Street, one of three connected townhouses on a small, blocked-off road in central London.

Downing Street is not like the White House. It is smaller, more crowded and much less grand, and the housing arrangements inside are more fluid.

Beginning with Tony Blair, who took office when he still had a young family, the last few prime ministers have lived in the apartment on the upper floors of 11 Downing Street, which is larger and more spacious than the pokier apartment at No. 10. That has relegated the chancellors of the Exchequer, who usually live in No. 11, to the apartment at No. 10.

Prime ministers typically provide many of their own furnishings, aided by public money for upkeep of their living quarters. Unlike in the United States, where the two-plus months between the presidential election and inauguration provide for a measured and organized housing transition, a change in premiership in Britain is abrupt. One prime minister moves out of Downing Street; the next moves in right away.

Last weekend, The Mail on Sunday reported that as a result of his divorce, Mr. Johnson “didn’t have any stuff” and had asked the government to pay for new furniture to fit out his prime ministerial apartment.

A spokesman told the newspaper that Mr. Johnson had been offered taxpayer-funded furniture but had turned it down, and that the prime minister would foot the bill for his own furnishings.

Sir Ed Davey, a member of Parliament from the opposition Liberal Democrat party, said he wanted to get to the bottom of the whole thing and planned to write to the Cabinet Office to find out what the government intended to spend on Mr. Johnson’s apartment.

“I’ve heard of sofa government, but this is ridiculous,” he told The Mail, using a Britishism for a leader’s circle of advisers. “He earns a fortune and should be able to earn his own furniture.”

In addition to his parliamentary salary, which is about 79,000 pounds a year, Mr. Johnson is reportedly paid 275,000 pounds a year for his weekly column in The Daily Telegraph and last year earned tens of thousands of pounds in speaking engagements. Those activities will most likely have to stop now that he is prime minister.

Declaring that Theresa May, the departing prime minister, had paid for her own furnishings and that “she has never earned anything like as much as Boris Johnson,” Mr. Davey alluded to accounts of Mr. Johnson’s fight with Ms. Symonds.

Neighbors said Ms. Symonds could be heard accusing Mr. Johnson of spilling red wine on her sofa and being spoiled about money.

“Rather than wine stain, he should be worried about the stain he is making on British politics,” Mr. Davey told The Mail.