It is "mission-critical" to follow social distancing rules to protect the NHS and slow the spread of coronavirus, Health Secretary Matt Hancock has said.
"The more people follow the rules then the faster we will all be through this," he said, after reports of packed public parks in London and elsewhere.
This morning Mr Hancock said such behaviour was "quite unbelievable".
At the daily Downing Street briefing, he said it could not go on. It comes as the UK death toll reaches 4,934.
The Department of Health said on Sunday there had been 621 more coronavirus-related deaths in the UK in the past day.
As of 09:00 BST on Sunday, 47,806 people had tested positive for coronavirus, the Department of Health said.
Mr Hancock said the government was "not planning any changes imminently" to social distancing policies but he "could not rule out further steps".
"What we are doing is being absolutely clear that the current rules must be followed,"
"So I say this to the small minority of people who are breaking the rules or pushing the boundaries: you're risking your own life and the lives of others and you're making it harder for us all."
Mr Hancock offered his "profound sympathies" to the families and friends of those who have died.
He added: "I've lost two people that I was fond of so I understand what a difficult time this is for the country.
"We need perseverance in the face of great challenges."
Speaking at the Downing Street briefing, Dr Jenny Harries, the deputy chief medical officer for England, said the rules in place were "the best way to be able to bend the curve down and stop the spread of the virus".
"It is not just what you are doing but how you are doing it," she added.
"If you are sitting on a park bench, people tend to accumulate - it is very difficult to prevent that."
It comes as Brockwell Park in Lambeth was forced to close on Sunday after more than 3,000 people spent the day there sunbathing or in large groups on Saturday.
There were similar scenes on Primrose Hill in Camden on Saturday, when police moved on more than 100 people.
But local officers tweeted to say thank you after finding far fewer crowds in the area on Sunday. And Brighton beach was nearly deserted on Sunday, following a warning by Brighton and Hove City Council that too many people were meeting up with friends on the seafront. It prompted a tweet from Sussex police thanking the public for heeding government advice. In Essex, local police echoed the sentiment, tweeting that "areas that would normally be busy on a sunny Sunday are not today".
Mayor of London Sadiq Khan has warned London parks will be forced to close if Londoners do not follow the rules on social gatherings, and urged people to stay at home amid the warm weather. Restrictions state that everybody must stay at home where possible, and only leave if they have a "reasonable excuse", such as exercise or shopping for basic necessities.
Newly elected Labour deputy leader Angela Rayner told Sophy Ridge it was "all right for people who have got big houses and huge back gardens" to tell sunbathers observing social distancing to stop doing so.
"If you're stuck in inadequate accommodation... and you're all on top of each other, quite literally, then I think people should do social distancing and should keep their distance, but also be reasonable and proportionate about that," she said.
Harriet Harman, MP for Camberwell and Peckham, has called for a rota for the use of public parks, writing on Twitter that families in flats with young children need green spaces during the lockdown.
Mr Hancock's warning came ahead of the Queen's address to the nation on Sunday.
In other developments:
Prime Minister Boris Johnson, who remains in self-isolation in Downing Street after testing positive for coronavirus, continues to have a high temperature but is "OK", Mr Hancock said
The new Labour leader, Sir Keir Starmer, has accused the government of making "serious mistakes" in its response to the coronavirus
Scotland's chief medical officer will step out of the public eye but remain in her role, after visiting her second home during the lockdown
The culture secretary is planning to hold virtual meetings with tech firms over their response to conspiracy theories linking 5G networks to the pandemic
The Foreign Office said it is now working with 14 commercial airlines to help thousands of Britons still stranded abroad amid the pandemic, with seven charter flights to bring travellers home from India in the coming week
Convenience stores on the outskirts of towns and in rural areas are experiencing a surge in sales - as people turn to them for essentials during the lockdown
A 54-year-old midwife who died with the virus in Essex on Thursday has been named as Lynsay Coventry, the Princess Alexandra Hospital NHS Trust said
A nursing assistant has died after looking after coronavirus patients at Watford General Hospital in Hertfordshire
Lord Bath of Longleat has died at the age of 89 after contracting coronavirus
The owner of London's ExCel centre has U-turned on charging the NHS to use the site as a hospital
New Labour leader Sir Keir Starmer said the party would support the government it if decides to toughen lockdown measures.
"We've got to get through this and every time people break the guidance from the government they put other people at risk," he said.
Prime Minister Boris Johnson, who is self-isolating after testing positive for coronavirus, tweeted his thanks to "everyone who is saving lives by staying at home this weekend".
"I know it's tough, but if we all work together and follow the guidance we will beat coronavirus," he said.
Mr Hancock said that the number of ventilators needed over the coming weeks will be 18,000, and that currently there are between 9,000 and 10,000 within the NHS.
When asked about the number of nurses that had died of coronavirus, Mr Hancock said the latest figure was three deaths.