The move plunges Boris Johnson into deeper jeopardy ahead of the publication of the investigation by Ms Gray, a senior civil servant in the Cabinet Office.
Dame Cressida told the London Assembly’s Police and Crime Committee: “We have a long-established and effective working relationship with the Cabinet Office, who have an investigative capability.
“As you well know they have been carrying out an investigation over the last few weeks.
“What I can tell you this morning is that as a result of the information provided by the Cabinet Office inquiry team and, secondly, my officers’ own assessment, I can confirm that the Met is now investigating a number of events that took place at Downing Street and Whitehall in the last two years in relation to potential breaches of Covid-19 regulations.”
Dame Cressida declined to say which alleged parties are being investigated, nor would she put a timeline on when officers could detail their findings.
“The fact that we are now investigating does not, of course, mean that fixed penalty notices will necessarily be issued in every instance and to every person involved,” she said.
“We will not be giving a running commentary on our current investigations.”
But there will be updates at “significant points”, she added.
Dame Cressida said “several other events” that appeared to have taken place in Downing Street and Whitehall had also been assessed, but they were not thought to have reached the threshold for criminal investigation.
It was not immediately clear whether the opening of the police investigation will further delay the publication of the inquiry, which had been expected later this week.
A Cabinet Office spokesman said: “The investigation being carried out by Sue Gray is continuing.
“There is ongoing contact with the Metropolitan Police Service.”
Dame Cressida said investigations are carried out into “the most serious and flagrant type of breach” where individuals knew they were committing an offence or “ought to have known”.
The Met had been under pressure to launch an investigation for weeks, with the Daily Mirror first reporting allegations of parties breaching coronavirus regulations taking place in No 10 two months ago.
Deputy Labour leader Angela Rayner questioned how Mr Johnson can remain Prime Minister with Downing Street under police investigation.
“Boris Johnson is a national distraction. Conservative MPs should stop propping him up and he should finally do the decent thing and resign,” she added.