Some 719 deaths registered in the seven days to May 13 mentioned Covid-19 on the death certificate, according to the Office for National Statistics (ONS).
This is down 2% week-on-week and is the lowest total since mid-March, when numbers were just starting to rise due to the surge in infections caused by the Omicron BA.2 variant.
The drop comes despite the latest figures including a backlog of deaths that needed to be registered following the bank holiday on May 2, when most council offices were closed.
The disruption to registrations caused by the bank holiday means the overall trend in the number of deaths is unclear.
But with Covid-19 infection levels having fallen sharply in recent weeks, past evidence suggests the death figures should soon show a steady decline.
The 719 deaths registered in the seven days to May 13 is around half the number reached at the peak of the initial Omicron wave at the start of this year, when 1,484 deaths were registered in the week ending January 21.
It is also well below the 8,433 deaths registered at the peak of the second wave of the virus, in the week to January 29 2021.
Overall, 197,534 deaths have now occurred in the UK where Covid-19 was mentioned on the death certificate, the ONS said.
The highest number on a single day was 1,488, on January 19 2021.
During the first wave of the virus, the daily toll peaked at 1,461 on April 8 2020.
Around nine in 10 deaths with Covid-19 on the death certificate since the start of the pandemic have coronavirus as the primary cause of death, with a minority listing the virus as a contributory factor.
The number of people in hospital in the UK with Covid-19 is now the lowest it has been since the start of October 2021, Government figures show.
Patients in mechanical ventilation beds have dropped to levels last seen almost a year ago, in mid-June 2021.