A further 413 people in UK hospitals who had been diagnosed with Covid-19 have died, bringing the overall death toll there to 20,732.
Health officials there have also announced an additional 4,463 confirmed cases.
There have also been five more deaths and 82 more cases in Northern Ireland, where the death toll now stands at 299.
British Environment Secretary George Eustice said that 669,850 Covid-19 tests had been carried out in the UK. Some 152,840 people have tested positive - an increase of 4,463 cases since the day before.
"15,953 people are currently in hospital with the coronavirus in the UK, down from 16,411 on April 25," he said.
"And sadly, of those hospitalised with the virus, 20,732 have now died, and that is an increase of 413 fatalities since yesterday."
Mr Eustice said lockdown measures would be reviewed in a couple of weeks but that it was very important not to act too soon.
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He refused to confirm if passengers entering UK airports will have to be quarantined for two weeks under the second phase of the British government's response to the coronavirus pandemic. He dismissed the report as "speculation".
Professor Stephen Powis, national medical director of NHS England, said the benefit of social distancing was beginning to be felt in the stabilisation of the number of new cases.
He added: "You can see we now have a very definite trend of a reduced number of people in hospitals - that is most marked in London.
"But there is the beginnings of that in the Midlands and other areas of the UK."
Asked why the UK Government did not record coronavirus-related deaths in care homes in the same way it has done for hospitals, Prof Powis said there was a "difference" in the way data is collected.
"In the NHS we work with several hundred hospitals to collect that data on a daily basis. We are collecting the data for people who have died in hospital who we know have tested positive. All those organisations are within the NHS family.
"In the care home sector, there are many, many thousands of care homes operated by many, many independent organisations, so that sort of daily rhythm of reporting in is just not something that occurs in care homes in the same way."
