Senior Tories have joined opposition MPs in demanding the report on No 10 lockdown parties be published in full.
MP Sir Christopher Chope accused the Met Police of an "abuse of power", amid concerns senior civil servant Sue Gray will leave out crucial findings.
Doubts over how complete the report will be came after the Met asked her to make "minimal reference" to events they are looking at.
A version of the report is yet to be handed to Downing Street.
While no exact timeframe for the report's submission has been given, Ms Gray is expected to submit her report before the Met finishes its investigations.
The force is investigating alleged parties and gatherings at Downing Street and other locations in Whitehall during coronavirus restrictions, and has received evidence from Ms Gray's team.
No 10 has pledged to publish Ms Gray's report "as they receive it".
Sir Christopher, the Conservative MP for Christchurch, accused the police of interfering with Ms Gray's investigation.
"They're not right [to ask for changes] this is not sub judice," he told BBC Radio 4's Today programme, referring to active legal proceedings that prohibit public discussion.
"If they had brought charges about individuals... then it would obviously be sub judice.
"That's why I think this is an abuse of power by the Metropolitan Police."
Senior Conservative MP Tobias Ellwood, who has been critical of the prime minister's handling of the issue, also warned that any redacted or watered down report would not "go down well with colleagues" and the public wanted to see the government was on the "road to change".
Another Tory MP Adam Holloway, who said he backs Boris Johnson but is willing to "run with" Ms Gray's findings, told Today: "If I was Boris I would be really quite desperate for the truth to get out."
It followed calls from Labour, the Liberal Democrats and the Scottish National Party for the report to be published without omissions.
Lord Morris of Aberavon, a former attorney general under ex-Labour PM Tony Blair, said he was dismayed with the police, telling the BBC: "Any prejudice which might result in fines would be a disproportionate concern."
But criminal barrister Matthew Scott, from Pump Court Chambers, said: "Given that they are investigating possible criminal offences I think they are absolutely right to do what they have done and ask.
"They have no power to enforce, but they can ask and they have done, that the relevant parts of the report not be made public before they have completed their inquiry."
In a statement on Friday night, the Met defended its request for the Cabinet Office to minimise reference to certain events in Ms Gray's report as being fair to those subject to investigation.
Commander Catherine Roper, who leads the Met's Central Specialist Crime Command, added: "This will only be necessary until these matters are concluded, and is to give detectives the most reliable picture of what happened at these events.
"We intend to complete our investigations promptly, fairly and proportionately.
"We have not delayed this report and the timing of its release is a matter for the Cabinet Office inquiry team."
Commander Roper said the offences under investigation would normally be dealt with by fixed penalty notice.
During the pandemic, fixed penalty notices ordered people to either pay a penalty - between £200 and £10,000 - or opt to face a criminal prosecution, usually at magistrate's court, for alleged breaches of Covid regulations.
Mr Johnson has said he welcomes the Met investigation and that it will "give the public the clarity it needs" over the allegations.
His spokesman said the prime minister did not believe he had broken the law.
At least 13 separate events are reported to have taken place at Downing Street or other buildings in Westminster when London, or the UK, were under tough restrictions.
Meanwhile, senior Conservative MP Tom Tugendhat has become the first MP to publicly say he would consider running for Tory leader if a contest was triggered.
Mr Tugendhat, who chairs Parliament's foreign affairs select committee, told Times Radio "it's up to all of us to put ourselves forward" but he added there was "not a vacancy at the moment" and said he had not been canvassing support.
Source: BBC News