It is too soon to see any impact of the recent slight rise in infections.
A total of 186 deaths registered in the seven days to June 3 mentioned coronavirus on the death certificate, according to the Office for National Statistics (ONS).
This is down 55% week-on-week and is the lowest number since July 2021.
The latest total covers a period that includes the bank holidays marking the Queen’s Platinum Jubilee on June 2 and 3, when most register offices were closed.
This means fewer deaths were registered than would normally be the case.
The disruption to registrations caused by the bank holidays is likely to have exaggerated the size of the week-on-week drop in registrations.
But it is the fifth week in a row the figures have shown a decrease, suggesting Covid-19 deaths are continuing on a clear downwards trend.
It is too soon to see any impact in death registrations of the recent slight rise in Covid-19 infections in some parts of the country.
Some 797,500 people in private households in England were likely to test positive for Covid-19 in the week ending June 2, the equivalent of about one in 70, the ONS said.
This is up week on week from 784,100, which was also about one in 70.
Infection levels are estimated to have risen in London, north-west England and south-east England, with early signs of an increase in eastern England.
Wales has seen Covid-19 infections increase very slightly to 40,500 people, up from 39,600, though both estimates are equivalent to around one in 75 people and the ONS describes the trend here as “uncertain”.
The rise in prevalence is likely to have been caused by the spread of the newer Omicron variants BA.4 and BA.5, along with a jump in infections compatible with the original Omicron variant BA.1.
The BA.2 variant – which caused a record wave of infections in spring this year – remains the dominant strain in the UK, however.
Separate figures show the recent fall in the number of people in hospital with the virus may have come to a halt.
Some 4,602 patients in England had Covid-19 on June 13, up 12% on the previous week, while in Wales the figure looks to have levelled off at around 250 to 260.
Patient numbers in both nations had previously been on a steady downwards trend since early April, following the peak of the Omicron BA.2 wave.
But they remain well below the levels reached in all previous waves of the virus.