The Metropolitan Police is to issue 20 fines to people who attended lockdown-breaking parties in Downing Street and Whitehall.
But the force has not named the individuals facing the penalties or revealed which events they attended.
Prime Minister Boris Johnson was among 100 people who were sent formal legal questionnaires relating to the investigation – named Operation Hillman – which was launched in January.
Read more: Everything you need to know about the police investigation into partygate
The probe related to 12 events where COVID restrictions may have been breached in 2020 and 2021.
Labour’s deputy leader Angela Rayner told Sky News on Tuesday that the Prime Minister or anyone in government must resign if they are fined.
A Met Police statement said: “The investigation into allegations of breaches of COVID-19 regulations in Whitehall and Downing Street has now progressed to the point where the first referrals for fixed penalty notices (FPN) will be made to ACRO Criminal Records Office.
“We will today initially begin to refer 20 fixed penalty notices to be issued for breaches of Covid-19 regulations.
“The ACRO Criminal Records Office will then be responsible for issuing the FPNs to the individual following the referrals from the MPS [Metropolitan Police Service].”
The Met said that with further evidence still to be assessed “further referrals may be made to ACRO if the evidential threshold is made”.
Ms Rayner said that Mr Johnson or chancellor Rishi Sunak or “anyone that’s in the government that decides to break their own rules” ought to resign if they are fined.
She told Sky News: “They were the rules that the prime minister made everyone follow.
“People couldn’t see their loved ones when they were dying.
“If the prime minister’s fined because he’s broken his own rules then I think his position’s untenable.
“I don’t think he can go to the British public and say ‘I’m acting in your own interest’ when he’s been laughing, joking, having parties and tried to lie about that.”
Earlier, government minister Will Quince acknowledged that “considerable upset” had been caused over events that “shouldn’t have happened” but was tight-lipped when asked if he thought the prime minister should resign if fined.
Mr Quince, who is minister for children and families, told Sky News: “That’s a hypothetical question, you wouldn’t expect me to answer that.”
The Prime Minister received a questionnaire on 11 February.
It is thought he attended as many as six of the events under scrutiny, but it is not yet clear whether he has received a fixed penalty notice.
Last week the Met confirmed detectives had begun interviewing key witnesses on details related to the questionnaire responses.
The 12 events under investigation took place over eight separate dates and include a “bring your own booze” event in the Downing Street garden on 20 May 2020, organised by the Prime Minister’s principal private secretary Martin Reynolds.
Another was a surprise birthday gathering for Mr Johnson in the cabinet room in June 2020, attended by the chancellor.
Fixed penalty notices do not amount to a criminal conviction, but they can result in court summons and criminal prosecution if they are not paid.
Several Conservative MPs had called for Mr Johnson to resign over the parties, but some have changed their stance since the war in Ukraine began just over a month ago.
Scotland Yard launched its investigation following the conclusion of the internal government inquiry led by senior civil servant Sue Gray.
A restricted version of her report was published at the end of January, but many details were removed so as not to compromise the police investigation.
It is unclear whether the full report will now be published.
The Prime Minister’s official spokesman has previously said discussions were needed “with the Met and others about what is suitable”.