John Newton, director of health improvement at Public Health England (PHE), said the initial method was meant to avoid underestimating COVID-19 deaths.
Under the new methodology, the number of deaths in people with Covid-19 that occurred within 28 days of testing positive will be published daily by the UK Government and devolved administrations. PHE and the devolved administrations also worked closely with the UK Statistics Authority on these new measures and the new approach is in line with advice from the statistics regulator.
In England, a person who died at any point following a positive test would previously have been counted in the toll, regardless of the Â cause of death.
Health Secretary Matt Hancock ordered an urgent review into how PHE calculated Covid-19 death figures after researchers criticised "statistical flaws" in the way England's deaths were reported.
But he said the new methods of calculating deaths from the virus would give "crucial information about both recent trends and overall mortality burden due to Covid-19".
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Public Health England said it made the change after discovering that "in recent weeks the numbers of deaths in people who have tested positive have become substantially greater than the numbers of deaths subsequently registered as COVID-19 deaths" by the Office for National Statistics, which uses death certificates to keep its tally.
But there will now be a cut-off of 28 days, providing a more accurate picture of the epidemic bringing England's measure in line with the other United Kingdom nations.
Professors Yoon Loke and Carl Heneghan raised concerns that anyone who had ever tested positive for Covid-19 and then died was included in England's death figures - even if they have died from something else. It brings the total number of coronavirus deaths in United Kingdom hospitals to 34,076 since the start of the outbreak.
"As Covid-19 deaths fall the number of recovered patients, particularly the very old and those with severe underlying conditions are now dying from these conditions and not Covid-19". Deaths that occur after 60 days will be included if Covid appears on the death certificate, it added.
The Department of Health and Social Care (DHSC) daily figures represents the number of reported deaths in all settings of people who have tested positive for Covid-19.