A total of 21,092 patients had died in hospital after testing positive for coronavirus in the UK as of 5pm on Sunday, Health Secretary Matt Hancock said.
The number of deaths is up by 360 from 20,732, the smallest increase since the end of March.
The latest figures are a decrease on Sunday's announcement, when it was confirmed 413 had died in the previous 24-hour period.
Chief medical officer for England Professor Chris Whitty said the country is not “consistently” past the peak of coronavirus deaths.
He said there was an “artificial drop” over the weekend typically seen because of lower notification rates.
“Nevertheless the trend overall … is a gradual decline but we’re definitely not consistently past the peak across the whole country at this point in time,” he added.
NHS England has announced 329 new deaths of people who tested positive for Covid-19, bringing the total number of confirmed reported deaths in hospitals in England to 18,749.
In Scotland, the figure rose by 13 from 1,249 on Sunday, Nicola Sturgeon said, while in Wales a further eight people have died after testing positive for coronavirus, taking the total number of deaths there to 796, health officials said.
Ms Sturgeon said 10,521 people have now tested positive for the virus in Scotland, up by 197 from 10,324 the day before.
There are 134 people in intensive care with coronavirus or coronavirus symptoms, an increase of one on Sunday, she added.
There are 1,762 people in hospital with confirmed or suspected Covid-19.
Ms Sturgeon added that 2,380 people who have tested positive for coronavirus have now been able to leave hospital.
She said the overall trend in statistics gives “cause for cautious optimism”.
Coronavirus: Everything you need to know