The country’s Office for National Statistics said there were 18,500 deaths in the week up to 10 April – around 10,000 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, 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”.
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.