Scotland Yard said by the end of the week officers from Operation Hillman will have started sending out formal legal questionnaires to more than 50 individuals.
The events under investigation include a number known to have been attended by Boris Johnson, raising the prospect that he will be among those receiving a demand for answers in their inboxes.
The announcement came after the Metropolitan Police said they would be widening their inquiries to cover a quiz night in No 10 in December 2020 after a photograph emerged of Mrs Johnson and colleagues near an open bottle of sparkling wine.
In a statement the force said the questionnaire would ask for “an account and explanation of the recipient’s participation” in an event which is the subject of police inquiries.
Recipients will be advised that the questionnaire has “formal legal status” and that they were required to respond “truthfully” within seven days.
In most cases the contact will be by email.
“If following an investigation, officers believe it is appropriate because the Covid regulations have been breached without a reasonable excuse, a fixed penalty notice will normally be issued,” the statement said.
“We understand the interest in and impact of this case, and are progressing the investigation at pace.
“We are committed to completing our investigations proportionately, fairly and impartially.”
An interim report last week by the senior official Sue Gray disclosed that police were investigating 12 different events in No 10 and Whitehall over the course of 2020 and 2021 for possible breaches of Covid rules.
They include the notorious “bring your own booze” event in the Downing Street garden in May 2020 attended by Mr Johnson and a gathering in the Prime Minister’s official flat in November 2020.
The Met said the Operation Hillman team was continuing to examine more than 500 documents and 300 images provided to them by the Cabinet Office and would be seeking further information to assist their inquiry.
Meanwhile it emerged that the Met is considering whether to investigate the funding of the lavish refurbishment of Boris Johnson’s official Downing Street flat following a complaint by lawyers acting for the Labour Party.
In a letter to Scotland Yard, the solicitors said there was a “reasonable suspicion” that the Prime Minister had broken anti-bribery laws which the force was “duty-bound” to investigate.
The Met confirmed they had received the letter which was being considered by officers from its Central Specialist Crime Command.
The complaint follows the release last month of an exchange of WhatsApp messages between the Prime Minister and Tory donor Lord Brownlow.
They show that Mr Johnson discussed a proposal supported by the peer for a Great Exhibition 2.0 at the same time as requesting his help with the £112,000 revamp of his official residence.
Ministerial records show that two months later, Lord Brownlow, who is a trustee of Royal Albert Hall Trust, attended a meeting with the then culture secretary Oliver Dowden to discuss the exhibition plan.
In his letter, seen by the Guardian, Gerald Shamash, of the law firm Edwards Duthie Shamash, said that despite inquiries by the Electoral Commission and Mr Johnson’s adviser on ministerial interests, Lord Geidt, there were still matters that were “uninvestigated and unconsidered”.
A Met spokesman said: “A letter was received and acknowledged on Friday February 4.
“It is being considered by officers from the Met’s Central Specialist Crime Command.
“No investigation has been opened.”
In response to the claims in the letter, a No 10 spokesman said: “These allegations are categorically untrue and a clear misrepresentation of the facts.”