But the low proportion of those testing positive for antibodies suggests such a move would allow only small numbers of people to move around more freely.
PHE said the earlier figures had excluded samples from blood donors aged over 70, who had been banned from giving blood when they were asked to stay at home during the lockdown. As a result, earlier figures showing the proportion of donors with antibodies appear to have given a misleading impression of the overall picture in the country.
The latest figures show that the overall proportion of people with antibodies is estimated at 6.5 per cent nationally in England.
The highest prevalence was in London, where 9.9 per cent of blood donors were found to have antibodies, compared to 6.5 per cent in the Midlands and 4.7 per cent in the north-east – down from an estimated 7.1 per cent earlier in the pandemic.
The data chimes with the latest findings from the Office for National Statistics, which said: "As of June 29, 6.3 per cent of individuals from whom blood samples were taken tested positive for antibodies to coronavirus (Covid-19)."
Addressing PHE's advisory board last week, Yvonne Doyle, its medical director, said: "We reckon that, over the peak, we had in London about 16 per cent of the population showing that they had antibodies.
"This is dropping off now, and it's now much lower than that. Overall, between six and 10 per cent of the population are showing those kind of antibodies as we do our regular seroprevalence testing."
Earlier this month, a study by scientists at King's College London found that Covid-19 antibodies peaked three weeks after the onset of symptoms and then begin to fade.
However, PHE said that while "waning immunity" may be a "contributory factor" in the drop in the prevalence of antibodies, it was "likely to play a relatively small role in the overall trends observed to date".
It added: "In more recent sampling periods, prevalence estimates are lower and this is likely to be largely driven by changes in the precise locations of sampling over time and potential demographic differences in the donor population as lockdown measures are relaxed.
"Regular donors aged 70 years and above were not allowed to donate during lockdown; this exclusion was lifted from week 26 [of 2020] and numbers of samples from donors aged 70+ have gradually increased from week 26 to date."
Some scientists have said large numbers of the population may have natural immunity against coronavirus even if they have never been infected.
Earlier this month, Sir John Bell, Regius Professor of Medicine at Oxford University, who is leading an Oxford team to develop a coronavirus vaccine (see above), told The Telegraph there was likely to be a "background level" of protection for a "significant number of people".
Recent studies have suggested the immune system can be primed by other coronaviruses, such as the common cold, giving the body a head start in fighting off Covid-19.
