Johnson, who won a landslide election victory in 2019, has faced intense scrutiny over the past month after a video emerged showing his staff laughing and joking about a different party also held in Downing Street during a 2020 Christmas lockdown.
Revelations about a series of gatherings that took place in the heart of government have been widely criticised and prompted opposition Labour Party leader Keir Starmer to accuse Johnson of lacking the moral authority to lead the country.
The latest, if substantiated by an internal inquiry, would be the most damaging yet for Johnson's future. His own lawmakers show signs of losing patience after a series of scandals, and polls show Johnson's Conservative Party slipping behind Labour.
Johnson and his partner Carrie were among those who gathered with about 40 staff in the garden of Downing Street on May 20, 2020, after the PM's Principal Private Secretary Martin Reynolds sent an invite by email using the pronoun "we", ITV reported.
Johnson's spokesman declined to comment on the report.
At the time, schools were shut to most pupils, and pubs and restaurants were closed, with strict controls on social mixing. Police prosecuted revellers, and people were prevented from bidding farewell in person to dying relatives.
"If the prime minister broke the law, he will resign won't he?" Labour lawmaker Ben Bradshaw asked Paymaster General Michael Ellis who sat alone on the government's front bench in parliament to answer in place of Johnson.
"The prime minister is going nowhere," Ellis said, to Labour jeers. Ellis apologised unreservedly for the upset that the allegations had caused.
Only a smattering of Conservative lawmakers attended the debate, and few spoke in support of Johnson.
Labour's Afzal Khan, asking if Johnson would apologise to bereaved families for holding such parties, related how his mother had died alone in hospital in 2020 while he sat in a car outside.
"Even burdened with our grief, my family obeyed the rules," Khan said.
A snap poll by Savanta ComRes showed 66% thought Johnson should resign, up 12 percentage points from a poll taken in December after the reports of Christmas parties. It said 42% of those who voted for Johnson in 2019 thought he should quit, up 9 points. The pollster interviewed a weighted sample of 1,040 adults online on Tuesday.
A YouGov poll of 5,391 people showed a similar increase in those who thought Johnson should quit - rising to 56% on Tuesday from 48% on Nov. 22.
A senior government official, Sue Gray, is currently investigating allegations of at least five parties held in government departments last year during lockdown restrictions.
Asked about the claims of Downing Street parties, Johnson told parliament last month that all COVID-19 guidance had been followed, no rules had been broken and that there had been no party in Downing Street.
Opponents said that if Johnson had attended a party during a lockdown, his position would be in danger as such revelry would show disdain for the rules.
"Did the prime minister attend the event in the Downing Street garden on May 20, 2020?," the opposition Labour Party's deputy leader, Angela Rayner, asked. "If the prime minister was there, surely he knew?"
Over recent months, Johnson, 57, has faced criticism over his handling of a sleaze scandal, the awarding of lucrative COVID-19 contracts, the refurbishment of his Downing Street flat and a claim he intervened to ensure pets were evacuated during the Western withdrawal from Afghanistan in August.
London police, who previously declined to investigate the claims of government officials' lockdown gatherings, said on Monday they were in contact with the Cabinet Office over the alleged breaches of health protection laws in Downing Street.
(Reporting by Alistair Smout and William James; Writing by Guy Faulconbridge; Editing by William Maclean, Catherine Evans and John Stonestreet)
By Alistair Smout and William James