Calls are growing for Sue Gray's report on No 10 parties to be published in full as soon as possible, amid wrangling over what it should contain.
Ms Gray had been expected to hand her report on alleged Covid-rule breaking to Boris Johnson this week.
But the Met Police have asked her to leave out key details to avoid prejudicing their own inquiries.
There is also debate in the Cabinet Office, where Ms Gray is based, about what should be redacted, sources say.
Labour leader Sir Keir Starmer is calling for the report to be published in full and the investigations to be wrapped up as soon as possible.
The SNP and Lib Dems are claiming the delay in publication is a "stitch-up" aimed at keeping Boris Johnson in power.
Many Conservative MPs are waiting to see the outcome of Ms Gray's inquiry before deciding whether to call for a vote of no confidence in him.
Met Police Commissioner Cressida Dick announced on Tuesday that the force was investigating several parties held during lockdown, after Ms Gray had suggested laws may have been broken.
The Met were understood to have had no objections to Ms Gray's findings being published in full.
But on Friday morning they issued a statement saying they had asked the senior civil servant to leave out certain details.
Analysis by politics correspondent Ione Wells
Sue Gray must now decide whether to publish a report that's been stripped of material relevant to the police inquiry or wait until the Met has given its verdict on the saga.
As a result, while No 10 has committed to publishing the report as they receive it, we don't now know if that will mean we will get it in full.
The Cabinet Office want to work carefully and respectfully with the police to make sure they do not do anything to infringe upon the police's inquiry.
Despite what seemed like a sudden intervention from the police this morning, taking even some in the Cabinet Office by surprise, this dialogue has been ongoing throughout Sue Gray's investigation - just as there have also been continuous discussions with HR and legal teams about what level of detail is appropriate for her report to include.
No 10 say they aren't privy to the discussions between the Cabinet Office and the police, and have not spoken to the Met themselves.
After a frenzy of speculation this week, one thing we can say with near certainty is the report now won't see the light of day this week - taking the imminent heat off Boris Johnson, for now.
"For the events the Met is investigating, we asked for minimal reference to be made in the Cabinet Office report," the force said.
"The Met did not ask for any limitations on other events in the report, or for the report to be delayed, but we have had ongoing contact with the Cabinet Office, including on the content of the report, to avoid any prejudice to our investigation."
Following the Met's intervention, it is unclear how much Ms Gray can say in her report, or when it can be published.
Sources have also suggested that wrangling within the Cabinet Office about the report, which is expected to contain criticism of the civil service, has also contributed to the delay.
The SNP's Westminster leader, Ian Blackford, claimed there had been "collusion" between the Cabinet Office and the Met police, telling BBC News: "This does look as if it's a stitch-up and the only person that benefits from that is Boris Johnson."
Liberal Democrat leader Sir Ed Davey said: "A stitch-up between the Met leadership and No 10 will damage our politics for generations and it looks like it is happening right in front of our eyes."
And Labour leader Sir Keir Starmer said: "What I want to see is Sue Gray's report in full and the investigation finished as quickly as possible".
Sir Roger Gale, who is among the Tory MPs to have publicly called for the PM to resign, described the latest developments as a "farce" which could delay a possible challenge to the "lame duck" prime minister.
Speaking on BBC Radio 4's The World At One, he added that unless there is a "legal barrier", the senior official should publish her report "now and in full".
Asked by the BBC's Nick Robinson if the police's statement was helpful to Mr Johnson, senior minister Jacob Rees-Mogg said: "It would be a very eccentric conspiracy theorist who thought that the prime minister being investigated by the police is beneficial for the prime minister - that is parallel universe stuff."
There have been media reports of 17 gatherings in government buildings while Covid restrictions were in place.
It has already been confirmed that the events Ms Gray is looking into include a "bring-your-own-booze" drinks event in the No 10 garden in May 2020 attended by Mr Johnson, and a staff gathering to celebrate the PM's birthday in June 2020.
Mr Johnson has promised that Ms Gray's report will be published "in full", and the prime minister's spokesman has also said Mr Johnson does not believe he broke Covid laws.
On Friday, Downing Street said it would publish the report it receives from Ms Gray's team, and added that it had not had any input into the Met's latest statement.
The PM's spokesman added that No 10 had not "been privy to the details" of Ms Gray's inquiry, or "any of its content".
Some Conservative MPs have demanded Mr Johnson's resignation, after weeks of reports of allegedly rule-breaking events in No 10 during lockdown.
But many others say they are waiting for the Gray report before deciding whether to submit letters of no confidence in him.
At least 54 Tory MPs must write to Sir Graham Brady, chairman of the backbench 1922 Committee, to set up a vote on the prime minister's future.
Meanwhile, it has emerged that former PM Theresa May told constituents she was "angry to hear stories of those in No 10, who are responsible for setting the coronavirus rules, not properly following the rules."
In a letter sent before the Met announced its investigation earlier this week, published by the Maidenhead Advertiser, she wrote that she expected "full accountability to follow" if Ms Gray's inquiry uncovered "evidence of deliberate or premeditated wrongdoing".