Deaths in England and Wales have nearly doubled above what would be expected, hitting a 20-year high.
The Office for National Statistics said there were 18,500 deaths in the week up to 10 April – about 8,000 more than is normal at this time of year.
More than 6,200 were linked to coronavirus, a sixth of which were outside of hospital.
But deaths from other causes also increased, suggesting the lockdown may be having an indirect impact on health.
Nick Stripe, head of health analysis at ONS, said they were trying to understand what had been happening with this increase in non-coronavirus deaths.
He said it could be that people with other illnesses were avoiding going to hospital treatment – visits to A&E have halved since the pandemic started.
But he added it could "take years to work out".
Mr Stripe said you have to go back to January 2000, when there was a bad flu season, to see a higher number of deaths in one week.
"Each one is a person. Each one has a family. We must always remember this," he added.
A similar trend is being reported in Scotland where there were nearly 2,000 deaths in the week up to 12 April.
Deaths in Northern Ireland are also up.
What does this tell us about coronavirus deaths?
This data is different from the daily death figures which are announced by government.
That looks at deaths in hospital where a person is infected with coronavirus.
The ONS figures rely on death certificates where the cause or contributory factors are listed.
As a result, the figures lag behind the government figures but give a fuller picture of what is happening.
They cover deaths in all situations – care homes and the community as well as hospitals – and so the figures are about a fifth higher than the government figures show.
Since the pandemic started, more than 1,000 deaths have been seen in care homes.
Overall a third of deaths during the week up to 10 April were linked to coronavirus.
More people have died from flu and pneumonia
Another way to judge the impact of coronavirus is to look at the overall impact on the numbers dying over the course of the year.
The figures show overall number of deaths are up. Nearly 185,000 people have died compared to around 175,000 on average compared to past five years – up until the pandemic hit the death rate was lower than average.