Former government adviser Prof Neil Ferguson will not face police action after he accepted making an “error of judgment” by breaching social distancing rules.
Scotland Yard said Prof Ferguson’s behaviour was “plainly disappointing”, but ruled out issuing a fine.
The force said he “has taken responsibility” after resigning as a government adviser on the epidemic.
Prof Ferguson said he regretted “undermining” social distancing rules.
The mathematician and epidemiologist’s modelling of the spread of coronavirus was key to the government’s decision to bring in the lockdown.
His resignation came after the Daily Telegraph reported that a woman he was said to be in a relationship with visited his home on at least two occasions during the lockdown.
In a statement, Scotland Yard said it was committed to supporting “adherence to the government guidance”.
But it added: “It is clear in this case that whilst this behaviour is plainly disappointing, Prof Ferguson has accepted that he made an error of judgment and has taken responsibility for that.
“We therefore do not intend to take any further action.”
The force declined to say whether it had spoken directly to Prof Ferguson.
Police officers are being advised to explain the law to those breaching the guidance, however, if someone refuses to follow the regulations police can issue an on-the-spot fine of £60.
Downing Street said Boris Johnson agreed with Prof Ferguson’s decision to resign, but denied that the government had pushed for him to step down.
The prime minister’s official spokesman said No 10 was informed “just before” the story broke on Tuesday.
Earlier, Health Secretary Matt Hancock described Prof Ferguson’s actions as “extraordinary”, telling Sky News that it was “just not possible” for him to continue advising the government.
He praised Prof Ferguson as a “very eminent” scientist whose work had been “important” in the government’s response but said social distancing rules were “there for everyone” and were “deadly serious”.
Prof Ferguson’s modelling of the virus’s transmission suggested 250,000 people could die without drastic action.
It led Mr Johnson to announce the lockdown on 23 March.
Under those measures, people were told to go out as little as possible, with partners who live separately later being told they should “ideally” stay in their own homes.
In a statement, Prof Ferguson said: “I accept I made an error of judgement and took the wrong course of action.
“I acted in the belief that I was immune, having tested positive for coronavirus and completely isolated myself for almost two weeks after developing symptoms.
“I deeply regret any undermining of the clear messages around the continued need for social distancing.”
He also called the government advice on social distancing “unequivocal”, adding that it was there “to protect all of us”.
Despite Prof Ferguson’s comments, it is currently unclear whether people who have recovered from the virus will be immune or able to catch it again.
BBC medical correspondent Fergus Walsh said “Neil Ferguson will know the science is very much developing” on immunity – and the government was not advising people to carry on as normal if they had already had the disease.
Sir Robert Lechler, president of the Academy of Medical Sciences, said he did not think Prof Ferguson’s resignation would “have any material impact” on the work of advisory group Sage.
He told the BBC that Prof Ferguson had made “an important contribution” but he was sure the group would “continue to provide valuable input”.
Prof Ferguson’s resignation comes a month after Scotland’s chief medical officer, Dr Catherine Calderwood, quit when it was revealed she had broken lockdown rules by making two trips to her second home.
Labour leader Sir Keir Starmer said it was right that Prof Ferguson had resigned.
“We all have a role to play in the fight against the virus,” Sir Keir’s spokesman said. “That means taking responsibility and following the official advice.”
Conservative MP Sir John Redwood suggested the circumstances behind Prof Ferguson’s resignation would not matter to the public.
“What matters to the nation is are we getting the right advice and how do we get through this dreadful crisis?” he said.