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LONDON — For a week, Prime Minister Boris Johnson of Britain has denied damaging claims that his staff broke lockdown rules by holding a party last Christmas when such festivities were banned under government-imposed coronavirus restrictions.

Late Tuesday, the government’s story weakened when a video surfaced of senior staff members joking about just such a party four days after they had reportedly gathered to eat snacks, drink wine and play party games in Downing Street.

The revelations have shaken Mr. Johnson’s government, coming just as Britain and the rest of the world enter a second holiday season battered by the emergence of a new variant and faced by anger and frustration from exhausted citizens.

The furor claimed its first casualty on Wednesday when Allegra Stratton, a senior aide, resigned. Ms. Stratton acknowledged that remarks she made in the video, at a time when she was Mr. Johnson’s spokesperson, seemed to make light of “rules that people were doing everything to obey.”

Most recently, Ms. Stratton had been spokesperson for the British government on the United Nations global climate summit in Glasgow known as COP26.

Later on Wednesday, Mr. Johnson of Britain announced major new restrictions to curb the spread of the coronavirus, urging people to work from home and introducing a vaccine passport for some indoor venues, measures that his government had long resisted.

Critics have accused Mr. Johnson of lying and trying to cover up the event in Downing Street last Christmas. There has also been anger from some Britons who, at the time, were prevented by lockdown rules even from saying farewell to dying relatives.

Downing Street has denied that a Christmas party took place but has not denied that there was an event of some kind. Mr. Johnson has said that any gathering that occurred followed Covid protocols.

At his weekly question-and-answer session at Parliament Wednesday, Mr. Johnson apologized for the video and said he was “sickened and furious” about it. But he said he was repeatedly assured that no party took place. He said the cabinet secretary, Simon Case, who is head of the civil service, would investigate and that if there were breaches of lockdown rules there would be disciplinary action.

Amid growing pressure on the prime minister, even some of his own lawmakers appealed publicly for him to get his story straight. On Tuesday night, the Metropolitan Police, the force that covers London, said it was reviewing the video.

The reports about the Downing Street party, which first appeared in the Daily Mirror, did not suggest that Mr. Johnson himself had attended any festivities. Nor does the video released by ITV, which shows staff members conducting a mock news conference with questions about the implications of holding such a party, completely confirm that an event occurred.

But the video shows that senior staff members were aware of the risk that they might be asked about a party in Downing Street and had no credible response. The video shows Allegra Stratton, who was then Mr. Johnson’s press secretary, at a rehearsal for a news conference, with a Downing Street colleague playing a journalist. At the time, Ms. Stratton was preparing to give White House style news conferences, though that idea was eventually abandoned.

When asked about reports of a Downing Street Christmas party, she laughed and replied: “I went home,” before asking, “What’s the answer?”

“Is cheese and wine all right? It was a business meeting,” Ms. Stratton can be heard saying. “This fictional party was a business meeting,” she continued, before laughing and adding: “And it was not socially distanced.”

Opponents have seized on the video as more evidence of a familiar and damaging critique: that the Conservative-led government applies one set of rules to itself and another to the rest of the population. That was deeply damaging early in the pandemic when faith in the government was seriously undermined after Mr. Johnson’s former chief adviser, Dominic Cummings, traveled hundreds of miles to his parents’ home during a lockdown.

In response to the video, the leader of the opposition Labour Party, Keir Starmer, accused the government of misleading the public. “People across the country followed the rules even when that meant being separated from their families, locked down and — tragically for many — unable to say goodbye to their loved ones,” he said.

“They had a right to expect that the government was doing the same,” he added. “To lie and to laugh about those lies is shameful.”No timescale has yet been given for the inquiry to be conducted by Mr. Case, the cabinet secretary. Nor does his remit extend to investigating reports about other parties in Downing Street including one that the Daily Mirror claims Mr. Johnson himself spoke at.