Many are elderly and would naturally be expected to die of age or other illnesses in the next few months or years.
Professor Heneghan said that if all are counted as Covid-19 deaths, the official PHE toll could well exceed 290,000.
The disparity helps explain why PHE’s out-of-hospital Covid death figures have remained stubbornly high, even though the Office for National Statistics shows deaths have been below the five-year average for the last three weeks.
Mr Hancock’s review piles further pressure on the besieged agency, which has come under massive criticism for failing to provide enough testing capacity until well into the crisis.
Speaking this morning on Today on BBC Radio 4, Professor Heneghan said: “We think it’s incredibly important, so that you understand exactly what’s going on, that you say these are the deaths that occurred within a certain time point, and then you can understand the trends and that will help the media report accurately to the public what’s going on.”
Asked what the real figures say about the shape of the epidemic, he added: “It has slowed in the last couple of weeks – it’s still coming down, but it’s coming down at a slower rate.
“The reason for that is not clear to us, but this is why we need correct stats accurate statistics so we can really understand the trend.
“If we get this massive variation it’s very difficult for us to understand exactly what’s going on.”