The London Metropolitan Police have received the material requested to support the investigation into possible lockdown breaches in Downing Street and Whitehall, the force has said.
Scotland Yard said officers would now examine the material "without fear or favour" to establish whether any rules were broken, adding that it had not delayed the publication of the Sue Gray report.
Commander Catherine Roper, who leads the Met's Central Specialist Crime Command, said the timing of the document's release was a matter for the Cabinet Office.
She said the force had asked for "minimal reference" to be made in the report to the "relevant events", in order to "protect the integrity of the police investigation" and be "as fair as possible to those who are subject to it".
"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," she said.
The force previously argued the constraints on Britain's Cabinet Office report into "partygate" were necessary to "avoid any prejudice to our investigation".
The new statement, issued this evening, contains no mention of the term "prejudice".
Ms Roper added: "We have not delayed this report and the timing of its release is a matter for the Cabinet Office inquiry team."
She said the offences under investigation, where proven, would normally result in the issuing of a fixed penalty notice.
"Individuals who are identified as having potentially breached these regulations will normally be contacted in writing, and invited to explain their actions, including whether they feel they had a reasonable excuse," she added.
"Following this process, and where there is sufficient evidence that individuals have breached the regulations without reasonable excuse, officers will decide if enforcement action is appropriate.
"If the decision is to take enforcement action then a report will be sent to the ACRO Criminal Records Office which will issue the fixed penalty notice. Recipients can pay the fixed penalty and the matter will be considered closed.
"Should a recipient dispute the fixed penalty notice then the case will be referred back to the Met where officers will consider whether to pursue the matter in a magistrates' court."
Scotland Yard's intervention to urge Sue Gray to limit the publication of her investigation had earlier faced widespread criticism.
Ken Macdonald, the former director of public prosecutions (DPP) for England and Wales, said the move seems "disproportionate" in the face of "very powerful" public interest in the report's swift publication, unless there is "more serious conduct" being investigated.
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Veteran Tory MP Roger Gale, one of the Conservatives to call for Mr Johnson's resignation, described it as a "farce" which could buy more time for the "lame duck" Prime Minister.
Opposition politicians warned of a "stitch-up" amid growing calls for the official report into potential Covid breaches in Downing Street and wider UK government to be published in full, with it having the potential to trigger a vote of no confidence in Mr Johnson.
Sources close to the inquiry have previously indicated Ms Gray was concerned about the prospect of releasing a report that was shorn of some of its key findings, raising the likelihood of a significant delay.
Officers have not confirmed how many events they are investigating, but reports have suggested it could be as high as eight.
Labour leader Keir Starmer, another former DPP, gave a measured response, calling for the full report to be published "as soon as possible" but conceding that "any issues of prejudice have got to be worked through".
A spokeswoman for Britain's Covid-19 Bereaved Families for Justice group accused the Met of letting bereaved families down as the Gray inquiry becomes "a circus".
Fran Hall said: "It's incredibly painful and they have let families like mine down. My husband was completely committed to justice, and he would have been appalled by this."
Liberal Democrat leader 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."
Downing Street said it had not had any conversations with the Met or the Cabinet office over what can be published.
The official inquiry was thrown into disarray on Tuesday when Met Police Commissioner Cressida Dick, who had long resisted calls to investigate, announced her officers had opened a criminal probe.
It was understood Ms Gray's team were still working on the investigation while in contact with the Met.
So far seven Tory MPs have publicly called for Mr Johnson to quit, but others are believed to have done so privately in letters to the chairman of the Conservatives' 1922 Committee.
If the number of letters received by Sir Graham Brady hits 54, representing 15% of all Tory MPs, then a vote of no confidence in the Prime Minister's leadership is triggered.
Mr Johnson would have to then win the support of half of Conservative MPs in order to stay in No 10.