Boris Johnson's top aide Dominic Cummings says he did the "right thing" by travelling 260 miles to be near relatives during the coranavirus lockdown.
Mr Cummings, who has said that he does not care what it looked like, is facing calls to resign over the journey, which he made with his wife who had Covid-19 symptoms.
Downing Street said he wanted to ensure he had childcare if he got symptoms.
The former chief constable of Durham has said it is clear that Dominic Cummings broke the lockdown rules with his trip from London to the north-east.
Mr Cummings told reporters he "behaved reasonably and legally" when asked about the trip from London to Durham.
Asked whether it looked good, he said: "Who cares about good looks? It's a question of doing the right thing. It's not about what you guys think."
Opposition parties have called for Boris Johnson to sack his chief adviser over the apparent lockdown breach, which was exposed by the Guardian and the Mirror.
Durham constabulary said it had spoken to Cummings’s family to remind them of the lockdown rules after receiving reports on 31 March that he was in Durham days after becoming ill.
In a statement, Downing Street said: "Owing to his wife being infected with suspected coronavirus and the high likelihood that he would himself become unwell, it was essential for Dominic Cummings to ensure his young child could be properly cared for.
"His sister and nieces had volunteered to help so he went to a house near to, but separate from, his extended family in case their help was needed. His sister shopped for the family and left everything outside.
"At no stage was he or his family spoken to by the police about this matter, as is being reported.
"His actions were in line with coronavirus guidelines."
Durham police tried to avoid punishing people for lockdown breaches. It has been one of the forces to issue fewest fines, at about 137 between 27 March and 11 May, compared with North Yorkshire police’s 843.
Durham Police and Crime Commissioner Steve White said it had been "most unwise" for Mr Cummings to make the journey, "given the whole ethos" of the government's guidance.
The Scottish National Party has called for Mr Cummings to quit or be fired - and has written to Sir Mark Sedwill, the head of the civil service, calling for a swift investigation into the incident.
The SNP's Westminster leader Ian Blackford said: "This is a matter of leadership and judgment for the prime minister who must prevent lasting damage to his government and his own reputation."
Senior government members have defended Mr Cummings on social media, with Cabinet Office Minister Michael Gove tweeting: "Caring for your wife and child is not a crime."
It comes after other high-profile figures involved in tackling the pandemic have resigned for breaching lockdown restrictions, including Scotland's former Chief Medical Officer Catherine Calderwood and leading scientist Prof Neil Ferguson.
Prof Ferguson also quit as a government adviser on coronavirus after it was reported that a married woman he was said to be in a relationship with visited him during lockdown.