As many as 100 people were invited to a “bring-your-own-booze” drinks event in the Downing Street garden during the first lockdown, it is understood.
Witnesses have told the BBC the PM and his wife were among about 30 people who attended the gathering on 20 May 2020.
But Boris Johnson has declined to say whether he was among those there.
The Metropolitan Police said it was in contact with the government over “widespread reporting relating to alleged breaches” of Covid rules.
Labour has been granted an urgent question in the Commons at 12:30 GMT to push for answers from a minister.
The party’s leader, Sir Keir Starmer, said the prime minister needed to “come clean” about the gathering.
Addressing Mr. Johnson on Twitter, he added: “Your deflections and distractions are absurd. Not only did you know about the parties in Downing Street, but you also attended them.
“Stop lying to the British public.”
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An email, revealed by ITV News, invited people to “socially distanced drinks in the No 10 garden this evening”.
It was sent when lockdown restrictions were still in place. Twelve days later – on 1 June – rules in England were relaxed to allow groups of up to six people to meet outside.
Health Minister Edward Argar told BBC Breakfast he understood the “anger, sadness and upset many will feel about these allegations”.
But he said it was “important” to allow an investigation to take place into gatherings in Downing Street before coming to any conclusions.
However, former Scottish Conservative leader Ruth Davidson told the BBC the PM did not need to wait for an inquiry to answer whether he attended.
“I can’t understand if the prime minister attended why on earth he thought that was the right thing to do,” she added.
“People are furious about this, what they gave up, how difficult it was, what happened to their own lives, and to think that this was going on? It is indefensible, it cannot be defended.”