"I don't want to have to take away exercise as a reason to leave home...if too many people are not following the rules," he told the BBC's Andrew Marr program.

"At the moment the vast majority of people are. But people should not break the rules because that would mean that the virus spreads more and we then might have to take further action."

There were fears that warm spring weather on Sunday could encourage Britons to head to parks. London's Lambeth Council closed Brockwell Park on Sunday after it said many people had sunbathed or gathered in large groups there on Saturday.

Hancock said it was "unbelievable" to see a small minority flouting the government's advice to maintain social-distancing.

If people did not follow the rules, which allow people to walk, run or cycle outdoors once a day but not sunbathe, he said he would have to ban exercise of all forms outside the home.

He said the timetable to ease restrictions - the lockdown exit strategy - could only be agreed once the spread of the coronavirus had been brought under control.

"Once we've flattened the curve in coronavirus cases we will be able to set out next steps. We are not there yet," he told Sky News.

Britain's death toll rose to 4313 on Saturday after 708 people died in the previous 24 hours, the highest daily rise so far.

Australian Associated Press