Dominic Cummings has insisted "I behaved reasonably and legally" after it was revealed he travelled 260 miles from London to Durham during lockdown.
When asked by reporters if his trip 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 [the media] think."
The PM's top aide, who emerged from his London home on Saturday holding a bicycle and ball, also told off reporters for not social distancing, telling them: "You're supposed to be more than two metres apart – move out of the way."
The prime minister's chief adviser is facing calls to resign after it emerged he left the capital with his wife and son to stay with his elderly parents in the North East – after developing coronavirus symptoms.
Durham Police confirmed they spoke to the owners of a property on 31 March – a week after the prime minister imposed the lockdown – after a call from someone reporting they had seen Mr Cummings in the area.
But Downing Street said nobody related to Mr Cummings was spoken to by police, and it was entirely right for him to seek childcare for his four-year-old son.
"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," Number 10 said in a statement earlier.
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"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. Mr Cummings believes he behaved reasonably and legally."
Transport Secretary Grant Shapps said: "Mr Cummings is in the public eye, but the reality of the matter is that a four-year-old child's welfare was the important thing.
"Parents ask themselves what they would do if they had if they no one else around and eventually you would have to turn to external support or try and be close enough to your family to provide that care, which is what happened in this
Analysis: Number 10 statement raises more questions
By Rob Powell, political correspondent
It's very hard to see how Mr Cummings has complied with coronavirus guidelines when rule number one is to stay at home and self-isolate if anyone in your household has symptoms.
Families who have struggled with the virus may wonder why the top adviser was not able to get help with shopping from family and friends at his London home, rather than making the 260-mile trip to Durham.
Downing Street has also not addressed who cared for Mr Cummings's young son after he had travelled to the North East.
Anonymous allies suggested last night that grandparents had helped. If true, that would be a further breach of lockdown rules, potentially exposing two vulnerable individuals to the virus.
Then there is the tacit accusation from Number 10 that Durham Constabulary lied to the press when it said officers had spoken to Mr Cummings's family about the trip.
Durham Police said it was standing by its statement when contacted by Sky News for a response to Number 10's version of events.
Officers were tipped off by a member of the public that Mr Cummings was staying with his parents.
"In line with national policing guidance, officers explained to the family the arrangements around self-isolation guidelines and reiterated the appropriate advice around essential travel," the force said.
Opposition parties said Mr Cummings "must go", and accused Downing Street of a "cover-up".
The SNP's Westminster leader Ian Blackford said he has written to the prime minister and the head of the civil service, Sir Mark Sedwill, calling for an investigation into the lockdown breach.
"Boris Johnson must answer serious questions about his role in this incident and the cover-up – including when he found out, when he heard about the police action, why Mr Cummings wasn't sacked immediately, and why he kept the public in the dark for eight weeks until a newspaper broke the story," he said.
"Dominic Cummings's position is completely untenable."
Sir Ed Davey, acting leader of the Liberal Democrats, told Sky News Mr Cummings "should either resign or the prime minister should sack him".
"I don't think there can be one rule for everyone else and a different rule for the prime minister's top team," he said.
"I can't see how Dominic Cummings is going to wriggle out of this one."
A Labour spokesperson said: "The lockdown rules were very clear: if you or anyone in your household was suspected of having COVID-19 you must immediately self-isolate and not leave the house.
"Number 10's statement also raises more questions than it answers. We are still unclear who knew about this decision and when, whether this was sanctioned by the prime minister and whether Number 10 is now questioning the validity of the statement from Durham Police."
Senior members of government voiced their support for Mr Cummings, including Health Secretary Matt Hancock, who tweeted: "I know how ill coronavirus makes you. It was entirely right for Dom Cummings to find childcare for his toddler, when both he and his wife were getting ill."
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