No. 10 has said ministers were not involved in the decision to pass on concerns about the events in Checkers and Downing Street to police following a review of the former prime minister’s official diary.
The Labor leader said Mr Johnson’s referral to the police over possible further breaches of the lockdown raises new questions.
Sir Keir Starmer, who visited Scotland on Friday, said the public was “fed up to the teeth” with stories about the former prime minister.
Sir Keir told broadcasters: “I think people are sick and tired of stories about Boris Johnson. At the heart of this is a simple truth that people across the country have made tremendous sacrifices during Covid.
“Some people don’t go to their baby’s birth, don’t go to the funeral of one of their close relatives.
“These are very personal things and the mounting revelations about Boris Johnson, I think, just add to that sense of hurt and people are fed up with it.
“I think now there are questions about why these allegations didn’t come out sooner, all these allegations.
“Of course there will be investigations, I understand that.
“At the heart of this is a very human sense of one rule for us, which we obey, another rule for Boris Johnson and those at the top of the Tory party.”
The Cabinet Office has said ministers “played no part” in the decision to hand over information to police, but that the referral was instead made by officials acting within the Civil Service Code.
Mr Johnson’s office has claimed the handling of the situation was “bizarre and unacceptable” and that the events in question were within the rules.
“It appears that some within the government have decided to make unfounded suggestions to both the police and the Privileges Committee,” a statement said.
“Many will conclude that this has all the hallmarks of yet another politically motivated conspiracy.”
Cabinet Office officials relayed their concerns to the Metropolitan Police and Thames Valley Police after the new information came to light during a review by taxpayer-funded lawyers ahead of the public inquiry into Covid.
The Privileges Committee, which is investigating whether Mr Johnson lied to parliament about the partygate scandal, has also been informed.
The Times reported on Friday that Mr Johnson had made preparations to release a photo of a particular garden visit to Downing Street in June 2020, which the paper said showed the then Prime Minister meeting his mother and sister for lunch.
Mr Johnson believed the image – which has now not been released – would have shown compliance with all rules, the paper said.