Excess deaths in England and Wales are at their lowest level since late March, according to the Office for National Statistics.
There were 12,288 registered deaths from all causes in the week ending 22 May - 2,348 more than the five-year average.
But the figure is well down on the height of the pandemic when weekly totals reached 22,351 deaths - nearly 12,000 more than normal.
Excess deaths measure the number recorded above the historical average.
Sky News economics editor Ed Conway said: "The gap is at the lowest it's been since the early days of this pandemic.
"So clearly you can see the mortality consequences are starting to abate now."
However, Conway added that across the whole of the UK since the pandemic began, figures show about 62,000 excess deaths from all causes - with around 48,000 put down to the coronavirus.
Of the latest 12,288 deaths registered in England and Wales, "novel coronavirus (COVID-19)" was mentioned in 2,589 (21.1%) of them - down from 3,810 (26.1%) the week before.
That is the lowest number of deaths involving COVID-19 in the last seven weeks, according to the ONS.
Care home deaths linked to the coronavirus fell from 37.2% of all deaths in that setting to 32.5%.
Looking at the outbreak as a whole over the last nine weeks, ONS head of health analysis Nick Stripe said the breakdown is:
The ONS records a coronavirus death whenever it is mentioned anywhere on the death certificate, including in combination with other health conditions.
It will not always be the main cause of death but may be a contributory factor.
A COVID-19 death will also be counted where the doctor completing the death certificate identified relevant symptoms and diagnosed a possible case of the disease, but no test was conducted.
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