The latest statistics show there were 6,391 deaths in care homes between 10 April and 1 May.
In Wales, there were a further 295 deaths in the same period.
Commenting on the latest figures, chairman of the Local Government Association's wellbeing board, Cllr Ian Hudspeth, said: ‘This appalling loss of life in our care homes and communities is another stark reminder of just how much more must be done to protect our most elderly and vulnerable.
‘Every death from this virus is a tragedy, leaving behind family and friends in mourning.
Social care is the frontline in the fight against coronavirus and we need to do all we can to shield people in care homes and those receiving care in their own homes.'
He urged the government to use councils' experience with track and trace in the on-going fight against coronavirus, and said it was vital for the Government to get its personal protective equipment ordering service up and running urgently to protect frontline workers.
Announcing the latest figures, the ONS said: ‘In the most recent days, the proportion of deaths occurring in care homes have accounted for over a third of deaths.
‘Although we expect numbers of deaths to increase as more are registered, it currently appears that deaths per day are decreasing.'
Assistant general secretary of Unison, Christina McAnea, urged the Government to provide more PPE for the care sector.
'It's not too late to save lives. The rate of infection can be reduced if care workers have proper access to protective kit,' she said. 'This would help stop the virus spreading between residents or being brought in from outside.
'But this can only happen if the government and employers ensure workers get the personal protective equipment they need. Testing also needs to be rolled out rapidly.'
