There were 379 deaths registered in the week ending April 2 where coronavirus was mentioned on the death certificate, the Office for National Statistics (ONS) said.
This is the lowest number since the week ending October 2 and down 5 per cent on the previous seven days.
The ONS said the number of deaths registered was affected by the Easter Monday bank holiday.
Around one in 24 (4.2 per cent) of all deaths registered in the week to April 9 mentioned Covid-19 on the death certificate.
Since the second wave peak, deaths involving Covid-19 occurring among people aged 80 and over have fallen by 97%, the figures suggest.
A total of 172 Covid-19 deaths in the 80-and-over age group occurred in England and Wales in the week ending April 2, down from 5,361 deaths in the week ending January 22.
Deaths for those aged 75-79 and 70-74 also dropped 97 per cent in the same period, compared with falls of 95 per cent for those aged 65-69 and 93 per cent for those aged 60-64.
Deaths that occurred in the most recent week of reporting – the week to April 9 – are still being registered.
The figure also show that 73 care home resident deaths involving Covid-19 were registered in the week to April 9, down 15 per cent on the previous week.
A total of 42,262 care home residents in England and Wales have now had Covid-19 recorded on their death certificate since the pandemic began.
The figures cover deaths of care home residents in all settings, not just in care homes.
The overall number of deaths registered was below the five-year average for the fifth consecutive week, the ONS said.
Some 9,098 deaths were registered in the week to April 9, 11.7 per cent below the average for the corresponding period in 2015-19.
The ONS warned that comparisons with the five-year average should be treated with caution as Easter bank holidays fall in different weeks each year.
A total of 151,795 deaths have now occurred in the UK where Covid-19 was mentioned on the death certificate, the ONS said.