The PM’s top aide Dominic Cummings might have broken lockdown rules, but it would have been a “minor breach”, say Durham Police.
Boris Johnson said he intended to “draw a line under the matter” following the police statement.
And he told reporters at the daily Downing Street briefing he did not want his scientific advisers to be dragged into a political row.
Opposition parties are continuing to call for Mr Cummings to be sacked.
Mr Johnson told the Downing Street press conference: “I’ve said quite a lot on this matter already and what I also note is that what Durham police said was that they were going to take no action and that the matter was closed.
“And I intend to draw a line under the matter.”
The prime minister stepped in to prevent his chief medical adviser, Chris Whitty, and his chief scientific adviser, Sir Patrick Vallance, from answering questions from journalists about Mr Cummings’ actions.
He told the BBC’s Political Editor, Laura Kuenssberg, who asked the advisers whether Mr Cummings was setting a good example, that he would intervene.
He said he wanted to “protect them from what I think would be an unfair and unnecessary attempt to ask any political questions”.
“It’s very, very important that our medical officers and scientific advisers do not get dragged into what I think most people would recognise is fundamentally a political argument,” he added.
Later in the briefing, Prof Whitty told another reporter he had no desire to “get pulled into politics,” a sentiment immediately echoed by Sir Patrick.
This was the first appearance of the two chief advisers at a Downing Street briefing since the Dominic Cummings story broke last Friday evening.
Labour leader Sir Keir Starmer said Mr Johnson should have allowed his advisers to answer journalists’ questions, adding: “We want transparency.”
“Nobody should be stopped from answering questions from journalists… but it’s the prime minister here that’s in issue, he’s been too weak throughout,” said the Labour leader.
He said he would have sacked Mr Cummings if he had been prime minster, and there had been a week of needless “distraction” from the safe easing of lockdown measures because Mr Johnson “has been frankly too weak to a draw line under this and take the necessary action”.
The SNP’s Westminster leader Ian Blackford said “one has to wonder what kind of democracy we are living in” when the prime minister blocks journalists’ questions, adding that Mr Cummings’ continued presence in Downing Street was “undermining public confidence in the health message”.
About 40 Tory MPs called for Mr Cummings to resign or be fired for undermining the government’s lockdown message and the prime minister’s authority.
By Helen Catt, BBC News political correspondent
This is a moment of maximum risk for the government and it comes at the end of a rocky week.
Boris Johnson clearly wanted to allay concerns over the timing of his lockdown easing announcement so we got a methodical briefing with graphs and stats to show how those “five tests” are being met.
But he also wanted to reinforce the message that the virus is still a threat. The government will have to hope that it has pitched that balance correctly.
The backdrop to all of this was, of course, the row over the PM’s adviser, Dominic Cummings, and if his trip to Barnard Castle might make that harder.
And this is where the briefing took a sharper turn.
For the first time in these press conferences, the PM took the extraordinary step of stopping the advisors flanking him from answering the questions posed by journalists.
He said it was to protect them (and they said they didn’t want to be drawn into it). Critics are likely to take a different view.
Mr Johnson clearly wants to draw a line under the events of the past week; the next few days will decide if that happens.
Mr Cummings’ decision in March to drive from his London home to his parents’ farm in County Durham with his wife – who had coronavirus symptoms – and his son, has dominated the headlines since the story broke on Friday night.
The PM’s chief adviser gave a news conference on Monday, explaining that he decided to make the trip because he felt it would be better to self-isolate in a place where he had options for childcare if required, and insisted he had acted “reasonably” and within the law.
He said he had made the 50-mile round-trip to Barnard Castle, with his wife and child, 15 days later to test his eyesight before embarking on the longer journey back to London.
In a statement earlier on Thursday, Durham Police said it did “not consider an offence was committed” when Mr Cummings drove himself and his family from London to Durham to isolate on his family’s farm.
His later trip to Barnard Castle “might have warranted a police intervention,” the force added, but it would not be taking any action against him now.
Durham Police said it regarded the likely breach of lockdown rules at Barnard Castle as minor because there was “no apparent breach of social distancing”.
“Had a Durham Constabulary police officer stopped Mr Cummings driving to or from Barnard Castle, the officer would have spoken to him, and, having established the facts, likely advised Mr Cummings to return to the address in Durham, providing advice on the dangers of travelling during the pandemic crisis.
“Had this advice been accepted by Mr Cummings, no enforcement action would have been taken.”
The force said it would not be taking retrospective action against Mr Cummings since this would amount to “treating Mr Cummings differently from other members of the public.”
Reports that Mr Cummings was seen in Durham on 19 April, suggesting a second trip from London, could not be support by evidence, the police statement added.
Mr Cummings has denied he was in Durham on that date.
BBC Home Affairs Correspondent Danny Shaw said it was understood that Durham Police examined other aspects of Mr Cummings’ stay in the area, including a possible breach of road safety laws and his trip to and from a hospital, where his son had received treatment.
“Its findings are not included in the statement – raising the prospect that the force has not quite managed to draw a line under the affair,” added our correspondent.