Police say Dominic Cummings may have committed 'a minor breach' of lockdown rules when he drove to Barnard Castle.
Prime minister Boris Johnson is standing by his senior aide despite Durham Police's findings.
The force has said that Mr Cummings will face no further action.
A statement from Durham Police said Mr Cummings' trip to Durham to self-isolate was not considered to be a breach of regulations, however his later trip to Barnard Castle may have been.
Mr Cummings has previously said he took the trip to the town, which is around 30 miles from where he was staying, in order to check that his eyesight was good enough to drive home to London.
A Number 10 spokesperson said: "The police have made clear they are taking no action against Mr Cummings over his self-isolation and that going to Durham did not breach the regulations.
"The Prime Minister has said he believes Mr Cummings behaved reasonably and legally given all the circumstances and he regards this issue as closed”.
The statement from Durham Police reads: "Durham Constabulary have examined the circumstances surrounding the journey to Barnard Castle (including ANPR, witness evidence and a review of Mr Cummings’ press conference on May 25 2020) and have concluded that there might have been a minor breach of the regulations that would have warranted police intervention.
"Durham Constabulary view this 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 statement added that the force had no intention of taking action against Mr Cummings "since this would amount to treating [him] differently from other members of the public".
Mr Cummings denies taking another trip to Durham on April 19, and Durham Police said they had 'insufficient evidence' to prove otherwise.
Anger within the Conservative Party has continued to mount, with at least 38 Conservative MPs calling for Mr Cummings to resign or be sacked.
Kim McGuinness, police and crime commissioner for Northumbria, warned that the public’s adherence to lockdown has been “undermined” by the row.
She told BBC’s Newsnight she was concerned the public’s attitude towards the lockdown had changed since his actions were revealed.
"We’re already anecdotally hearing from MPs, from the media, from police officers that people are using Dominic Cummings as an excuse when they’re approached about why they’re breaking lockdown rules," she said.
