Johnson, who in 2019 won the biggest Conservative majority in more than 30 years, is facing a raft of accusations that he and his staff partied during the worst pandemic for a century and a complaint of racist discrimination in his party.
The new allegation come just days before an official investigation by Cabinet Office official Sue Gray into the lockdown parties is due to be published later this week.
ITV News said up to 30 people attended the June 2020 birthday event, during the first COVID lockdown, in 10 Downing Street, his central London office and residence. Social gatherings indoors were banned at the time.
The prime minister was believed to have been presented with a cake while his wife led staff in a chorus of happy birthday, it said.
Johnson's office disputed that it was a party, telling ITV: "A group of staff working in No. 10 that day gathered briefly in the Cabinet Room after a meeting to wish the prime minister a happy birthday."
"He was there for less than 10 minutes," it said.
ITV said there was another gathering in Downing Street the evening before his birthday. Johnson's office said that was "totally untrue".
Johnson has given a variety of explanations about the previous allegations of parties: first he said no rules had been broken but then he apologised to the British people for the apparent hypocrisy of such gatherings.
Police officers who guard Downing Street have been interviewed by Gray and have given "extremely damning" evidence, the Telegraph newspaper reported, citing an unidentified source.
"Johnson has completely lost his authority," Nick Timothy, who served as Downing Street chief of staff to Johnson's Conservative predecessor Theresa May, wrote in the Telegraph.
"The collapse in Johnson's authority is causing widespread political dysfunction and further danger for the Conservatives," he said. "Johnson is no longer popular, he is no longer powerful."
Johnson has denied an allegation that he was told a "bring your own booze" lockdown gathering on May 20, 2020, which he says he thought was a work event, was inappropriate.
His former senior adviser Dominic Cummings - now a harsh critic - said on Monday he was answering questions from Gray in writing.
Toppling Johnson would leave Britain in limbo for months just as the West deals with the Ukraine crisis and the world's fifth largest economy grapples with a once-in-a-generation inflationary wave.
To trigger a leadership challenge, 54 of the 359 Conservative MPs in parliament must submit letters of no confidence.
Leading rivals within the Conservative Party include Chancellor of the Exchequer Rishi Sunak, 41, and Foreign Secretary Liz Truss, 46.
Johnson on Monday ordered an inquiry into allegations by a lawmaker who said she was fired from a ministerial job in the government partly because her Muslim faith was making colleagues uncomfortable.
Nusrat Ghani, 49, who lost her job as a junior transport minister in February 2020, told the Sunday Times that she had been told by a "whip" - an enforcer of parliamentary discipline - that her "Muslimness" had been raised as an issue in her sacking.
The government's chief whip, Mark Spencer, said he was the person at the centre of Ghani's allegations. He said they were completely false and defamatory.
"I have never used those words attributed to me," he said.
Johnson met Ghani to discuss the "extremely serious" allegations in July 2020, a spokesperson from the prime minister's office said on Sunday.
Downing Street said that when the allegations were first made, Johnson recommended she make a formal complaint to the Conservative Campaign Headquarters.
"She did not take up this offer," Downing Street said.
Ghani's allegation came after one of her Conservative colleagues said he would meet police to discuss accusations that government whips had attempted to "blackmail" lawmakers suspected of trying to force Johnson from office.