The force is investigating a gathering in the Durham office of Labour MP Mary Foy in April 2021, when most indoor socialising was banned.Sir Keir was caught on camera drinking a beer after a day of campaigning for the local elections.
Ms Rayner was also at the event, dubbed by some as “beergate” in the wake of the Downing Street “partygate” investigation into lockdown breaches - which saw the Boris Johnson, wife Carrie, and Rishi Sunak, fined by police.
Neither the PM nor the Chancellor resigned over the issue.
Both the Labour leader and his deputy have said they will stand down if fined by police over the investigation - but the pair have insisted they are "confident" that no rules were broken.
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Sir Keir has previously said he “put everything on the line” by promising to step down if he receives a fixed penalty notice, and that resigning would be “the right thing to do”.
"I'm absolutely clear that no laws were broken, they were followed at all times," Sir Keir has said.
At the time of the Durham gathering, non-essential retail and outdoor venues including pub gardens were open, but social distancing rules – which included a ban on indoor mixing between households – remained in place.
Footage of the incident shows the Labour leader holding a beer
But Labour has argued that food was consumed between work events, meaning it was within the rules.
Labour has sought to contrast Sir Keir’s actions with those of Boris Johnson, who has refused to quit after being fined by the Met Police over a gathering in No 10 in June 2020 to mark his 56th birthday.
Labour sources are confident they can prove the Durham event was work-related and that those present were taking a break to eat while working late on preparations for the Hartlepool by-election.