Of these, 2,912 (25.3 per cent) mentioned “novel coronavirus” on the death certificate.
The ONS said the figures for the most recent week should be interpreted with caution as they had been affected by the Christmas Day bank holiday.
The number of deaths traditionally falls between these weeks, it added.
The number of deaths involving Covid-19 fell in five regions in England, but continued to rise in the North East, East and London, and Wales.
The seven-day Covid rate has spiralled above 1,000 new cases per 100,000 people in 12 boroughs.
It rose to 1,496.4 in Barking and Dagenham in the week to December 31, the highest rate in the country, 1,398.3 in Redbridge and 1,275.2 in Newham as the epidemic continues to hit the east of the city particularly hard.
The rate reached 971.3 for London as a whole.
Registered deaths in all locations – hospitals, care homes, private homes and elsewhere – were all above the five-year average for this week.
England’s lockdown has already come into force and MPs will vote later to retrospectively approve it with very little resistance expected.
Mr Johnson told the House Of Commons: “Our emergence from the lockdown cocoon will not be a big bang but a gradual unwrapping.
“That is why the legislation this House will vote on later today runs until March 31 – not because we expect the full national lockdown to continue until then but to allow a steady, controlled and evidence-led move down through the tiers on a regional basis.”
Additional reporting by PA