Matt Hancock has warned people could be forced to self-isolate under the new coronavirus test and trace system if they do not follow the rules voluntarily.
The health secretary predicted the "vast majority" will comply with the new strategy to loosen lockdown in England as he laughed off suggestions it was rushed forward to distract from the row over Downing Street aide Dominic Cummings.
He told Sky News' Kay Burley@Breakfast the suggestion was "priceless".
Speaking on the day of the launch of the contact tracing drive, he said: "We have considered making this mandatory and there are some other countries in which it's mandatory.
"But in the first instance we have great faith the public will follow the instructions from the NHS…
"It's an instruction from the NHS and it's very important that you do it, but it's legally not mandated at this stage because we think it's far, far better if as a country we pull together and do this and everybody follows the instructions."
Mr Hancock dismissed calls from a growing number of Tory MPs – which now include a senior minister – to sack Boris Johnson's top adviser for making three trips during lockdown which "undermined key public health messages".
More from Covid-19
Security minister James Brokenshire released a statement saying "no-one is above the law" and "ultimately it is for the police to determine" whether Mr Cummings broke it, as a former cabinet minister Karen Bradley said he should go to "stop damaging the work that needs to be done".
"It's about the future – that's actually what matters," Mr Hancock insisted on Thursday.
Mr Hancock claimed an app that monitors if a person has been near someone with COVID-19 will be expanded from its Isle of Wight trial soon but is not essential. "It puts the cherry on the cake, it isn't the cake," he explained.
Asked what people should do if they have childcare issues but are told to self-isolate, Mr Hancock told Sky News: "Well, of course, it is very important that childcare is taken into account.
"I understand that as well as anybody, so yes it is very important that people deal with childcare and do that in a reasonable way."
Pushed on if they would need to stay at home, he added: "That is what you will be instructed to do, yes, and you should follow those instructions because that is in the best interest of everybody."
Mr Cummings said earlier this week he had "exceptional circumstances" to move from London to his parents' farm in Durham to seek childcare help, and claimed he drove 30 minutes to the town of Barnard Castle to test his eyesight.
Britons have been in lockdown for 66 days, following the point on 23 March where the government moved from trying to contain outbreaks to delaying them spreading across the country.
The emergency measures are due to be reviewed today, after at least 37,460 people in the UK died with the virus – the worst death toll in Europe and second highest in the world.