Matt Hancock said it was people's "civic duty" to self isolate if they are asked to in the future.
At Tuesday's daily coronavirus press conference, the Health Secretary was asked about Dominic Cummings, the Prime Minister's chief advisor who said he had "no regrets" about travelling 260 miles in lockdown.
On Monday, Mr Cummings said his actions were within the lockdown rules set out by the Government and that a 30 mile trip to Barnard Castle while he was in Durham was to test his eyesight.
Mr Hancock faced numerous questions from journalists about Mr Cummings and defended asking the public to self-isolate in the upcoming test and trace programme despite the aide's actions.
When asked why people should follow government advice if they are asked to stay at home and self isolate under a future contact tracing system, Mr Hancock told the Downing Street briefing: “They’re not doing it for me, people are doing this for their loved ones.
“If you’re phoned up and asked to self-isolate even though you’re perfectly healthy because you’ve been in close contact with somebody who’s tested positive, then it’s your civic duty to then self-isolate, for yourself, for your community, for your family, and we all need to come together to do this.”
Matt Hancock said the lockdown guidelines were drafted with “exceptional circumstances” in mind – allowing for the defence that Dominic Cummings had used.
“It is reasonable to conclude that the description of events that Mr Cummings put out yesterday was within the guidelines,” Mr Hancock said.
But he added: “I understand that reasonable people will disagree with that and of course I understand some of the anger that boiled up over the weekend”.
Mr Hancock told the briefing he believes that Mr Cummings acted within the guidelines set out by the Government.
He said: “My view is that what he did was within the guidelines.
“I can understand why reasonable people can take a different view, but my judgement, which is the same as the Prime Minister’s judgement, is that what Mr Cummings did was within the guidelines.
“After all, the guidelines allow for exceptional circumstances, particularly with regards to childcare and we’ve stated before that if you’re unable to look after a small child, that is an exceptional circumstance.”
He said he understood the “anger that some people feel” over Dominic Cummings actions.
“I regret the anger that some people feel and Mr Cummings himself said that – with hindsight – he should have got all the facts out earlier,” Mr Hancock said.
But he said his focus was on the next steps in tackling the crisis.
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