It comes after ITV released new pictures showing the PM raising a glass at a leaving do on 13 November 2020.
The police watchdog has been urged to review the Met’s handling of the Partygate investigation.
Meanwhile, civil servant Sue Gray’s report into No 10 parties is imminent, a Downing Street source said.
The prime minister and the Met are under fresh scrutiny after ITV News published four new photographs on Monday it says were taken at the leaving do for Mr Johnson’s communications chief, Lee Cain.
Mr Johnson is pictured toasting colleagues while standing by a table laden with wine bottles and wine glasses.
A second coronavirus lockdown was in place in England at the time the photographs were taken, with indoor gatherings of two or more people banned, except if “reasonably necessary” for work purposes.
The BBC has been told that at least one person who attended the event has received a fixed penalty notice, but Mr Johnson has not. The Met has declined to explain why the prime minister was not fined over the leaving party.
The Liberal Democrats have written to the Independent Office for Police Conduct, urging it to investigate the Met’s probe into events in No 10 and Whitehall during lockdown.
The party’s deputy leader Daisy Cooper said: “If anyone else had been pictured at a party like this during lockdown, surely this would have been enough evidence for them to be fined.
“It does seem that there has been one rule for the prime minister and another for everyone else.”
A No 10 spokeswoman said the Cabinet Office and the police had been given access to information, including photographs.
The emergence of the photographs has sparked fresh claims from opposition MPs and others that Mr Johnson knowingly misled Parliament when he previously told them no Covid rules had been broken in Downing Street.
The prime minister faces a probe by the Commons’ Privileges Committee about whether he lied to MPs. Under government guidelines, ministers who knowingly mislead Parliament are expected to resign.
Responding to the leaked pictures, Labour’s deputy leader Angela Rayner said the PM had “demeaned his office” and that “the British people deserve better”.
The peer and former leader of the Scottish Conservatives, Ruth Davidson, said the prime minister’s position was untenable, while veteran Tory MP Sir Roger Gale said the new images were “damning” and suggested Mr Johnson should quit.