Matt Hancock has warned the coronavirus lockdown measures could be tightened if people fail to observe them properly.
The health secretary said on Sunday that outdoor exercise could be banned if people flout the social distancing rules.
Appearing on television, Mr Hancock said sunbathing in public spaces was against the Government guidance, and told those who dared to disobey that they are putting their own and others’ lives at risk.
It comes as one London council has been forced to close one of the city’s largest parks after 3,000 “sunbathers” ignored the strict coronavirus lockdown measures on Saturday.
Lambeth Council tweeted that Brockwell Park in Herne Hill, south London would be shut from Sunday onwards.
Mr Hancock told the BBC: “We’ve said it’s OK to go for exercise because both the physical and mental health benefits of getting some exercise are really important.
“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.
“At the moment the vast majority of people are (following the guidance) but people should not break the rules because that will mean that the virus spreads more and then we might have to take further action.”
He added that the “vast majority of the public” were following guidance to stay at home unless they are going to buy essentials such as food or medicine, seeking medical care, going to work, or exercising.
Lambeth Council claimed around 3,000 visitors descended on the park on Saturday, many of whom were “sunbathing or in large groups”.
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The council announced the news on Twitter, describing the revellers' behaviour as "unacceptable."
“Despite clear advice, over 3000 people spent today in Brockwell Park, many of them sunbathing or in large groups,” a Lambeth council spokesperson tweeted.
"This is unacceptable. Unfortunately, the actions of a minority now means that, following police advice, Brockwell Park will be closed tomorrow. #StayHome."
Images posted on Twitter on Saturday showed crowds of people in London Fields and Battersea Park in the capital, with some seen sunbathing and others on hire bikes.
In the North East, surfers were pictured on the beach at Tynemouth.
Speaking at the daily Downing Street press conference, Cabinet secretary Michael Gove urged people to consider the current pressure on the NHS, and to ask themselves: “How am I helping in this shared national effort?”
He added: “I know that lockdown is challenging, I know it’s very difficult, particularly for families with children.
“But people must at every stage respect these guidelines because that is the only way of making sure we restrict the spread of the disease.”