A further 77 people have died in the UK after testing positive for coronavirus - the lowest daily increase since the lockdown began.
No new coronavirus deaths were recorded in Scotland or Northern Ireland.
Experts say the number of deaths recorded over weekends tends to be lower because of reporting delays.
And earlier, a scientist advising the government said there was still "an awful long way to go" before the pandemic would end in the UK.
Professor John Edmunds said there was a risk the disease will "come back very fast" if the UK "relaxed its guard".
And he said he wished the UK had gone into lockdown sooner as the delay "cost a lot of lives".
A total of 40,542 people have now died after testing positive for the virus the UK.
The UK is only the second country - after the US - to reach 40,000 deaths.
The last time Scotland recorded no new deaths was on 20 March - three days before the lockdown was announced.
Scottish Health Secretary Jeane Freeman gave a "note of caution" about reading too much into Sunday's figures.
She said: "It is still very likely that further Covid-19 deaths will be reported in the days ahead."
NHS England announced another 72 deaths and Wales announced five.
The daily figure only includes those who have tested positive for the virus, and other figures show the death toll could be higher.
Data from the Office for National Statistics (ONS), which counts death certificates mentioning the virus, suggests deaths had reached more than 48,000 by 22 May.
It has been just over three months since the UK recorded its first coronavirus death on 2 March.
Health Secretary Matt Hancock rejected the comments by Prof Edmunds, who sits on the government's Scientific Advisory Group for Emergencies (Sage).
He insisted: "I think we took the right decisions at the right time."
Mr Hancock added that there were more than 100 members of Sage, and said the government had been guided by the balance of scientific opinion from the group.
Meanwhile, the government says it has now reached its target this weekend of delivering tests to all staff and residents of care homes.
Mr Hancock said coronavirus test kits have been offered to every care home in England and have delivered tests to 9,000 eligible care homes.
But Labour's shadow minister for social care, Liz Kendall, said the original pledge had been for tests to have been carried out, not just delivered to care homes, and accused the government of being "too slow to act".
The pledge was made on 15 May, when Mr Hancock said all residents and members of staff in care homes in England would have been tested for coronavirus by early June.
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