Angela Rayner was at a lockdown event with Starmer
Labour deputy leader Angela Rayner was at an event where Sir Keir Starmer was filmed drinking a beer during lockdown last year, the party has said.
It had previously denied she was at the event, but now says that statement was a "mistake" made in "good faith".
Labour leader Sir Keir said no rules were broken at the April 2021 gathering in a Durham MP's constituency office.
But Tory MPs are urging police to review their decision to not investigate the event.
Richard Holden, MP for North West Durham, wrote to Durham police last week asking them to reconsider after London's Metropolitan Police fined Prime Minister Boris Johnson for breaching lockdown rules at a June 2020 party in Downing Street.
This week Durham police said they would consider and respond to "further communications" on the matter, but were not "currently investigating this incident".
Earlier this year Durham police said they did not believe any offence was committed at the event on April 30, 2021, when Sir Keir was pictured with a bottle of beer in the office of City of Durham MP Mary Foy ahead of the Hartlepool by-election.
The party said Sir Keir was in the workplace, meeting a local MP in her constituency office and participating in an online Labour event.
Asked about the event on Friday, Sir Keir told reporters "everything we the Labour party did was in accordance with the rules".
"Whether Angela Rayner was there or not makes absolutely no difference. There was no breach of the rules, the matter's already been looked into.
"I know what's going on here. We're a few days away from local elections, and Conservative MPs are trying to throw as much mud as possible".
He added there was a "huge contrast" between the Durham event and lockdown parties in government buildings - for which Met police have issued more than 50 fines so far.
Labour has previously said there was a brief break for food and no Covid rules were broken, because there was an exemption for events held for "work purposes".
But in his letter to Durham police, Mr Holden argued that "this location was not the usual workplace" of Sir Keir, and there was "no necessity" for him to attend the event.
On Friday, the Daily Mail reported that Labour had acknowledged Ms Rayner had also been present at the online rally in the Durham offices where Sir Keir had been filmed drinking a beer.
A Labour spokesman told the BBC their initial response to the Mail's questions had been "a mistake" and not a cover-up, because Labour would have had no reason to conceal Ms Rayner's attendance as no lockdown rules had been broken.
The spokesman would not comment on whether the party or leader's office had been in contact with Durham police, but pointed out there has been no new investigation.
What were lockdown rules on 30 April 2021?
On 30 April, England was in the "Step 2" rules, which had been introduced on 12 April.
Gathering indoors with people from outside your household or support bubble was against the law.
There was an exemption for "work purposes", although working from home was recommended in the guidance. The rules did not mention socialising at work.
The question for police would have been whether Labour officials eating and drinking together would have been "reasonably necessary for work" and whether drinking beer makes a difference to that.
Keir Starmer told LBC Radio that as pubs and restaurants were closed and his hotel was not serving food, "if you didn't get a takeaway then our team wasn't eating that evening".
Bars, pubs and restaurants were allowed to open outdoors for groups of six people or two households, but indoor service was not allowed.
Durham Police reviewed the video in February this year and said it did not believe an offence had been committed.
The rules on indoor gatherings were the same in June 2020, when Boris Johnson attended a gathering for his birthday, for which he was fined. Gatherings of two or more people indoors were banned by law unless they were reasonably necessary for work purposes.
Labour have attacked Prime Minister Boris Johnson over his attendance at parties in Number 10 when Covid restrictions were in force.
Earlier this month the Metropolitan Police fined Mr Johnson and others - including Chancellor Rishi Sunak - for attending a birthday party arranged for the prime minister in Downing Street in June 2020.
Restrictions at the time banned most indoor gatherings involving more than two people.
Mr Johnson said he had paid the fine, offered a full apology, and promised to "get on and deliver the mandate that I have".
But Sir Keir and other opposition party leaders demanded the prime minister's resignation and accused him of lying to the public about his attendance at the Downing Street gathering.
Some Conservative MPs have called for Mr Johnson to stand down, but cabinet ministers have been supportive, saying the prime minister should stay in office.
The fines were part of an investigation by the Metropolitan Police into 12 gatherings across Whitehall during Covid lockdowns in 2020 and 2021.