Here, it seems that PHE regularly looks for people on the NHS database who have ever tested positive, and simply checks to see if they are still alive or not. PHE does not appear to consider how long ago the COVID test result was, nor whether the person has been successfully treated in hospital and discharged to the community. Anyone who has tested COVID positive but subsequently died at a later date of any cause will be included on the PHE COVID death figures.
By this PHE definition, no one with COVID in England is allowed to ever recover from their illness. A patient who has tested positive, but successfully treated and discharged from hospital, will still be counted as a COVID death even if they had a heart attack or were run over by a bus three months later.