A total of 853 deaths registered in the seven days to April 1 mentioned Covid-19 on the death certificate, according to the Office for National Statistics (ONS).
This is up 9% on the previous week and is the second clear week-on-week increase.
The figures suggest deaths are now on an upwards trend, following several weeks where the numbers appeared to have levelled off.
Prevalence of coronavirus is currently near or at record levels across most of the UK, following a surge in infections driven by the Omicron BA.2 variant.
This is now likely to be having an impact on the number of death registrations.
The total for the week to April 1 of 853 is the highest since 863 deaths in the week to February 18.
During the previous surge of infections at the start of this year, which was caused by the original Omicron variant, Covid-19 deaths registered in England and Wales peaked at 1,484 in the week to January 21.
But this was well below the 8,433 deaths registered at the peak of the second wave of the virus, in the week to January 29 2021.
The relatively low number of deaths during recent months reflects the success of the vaccination programme, in particular the rollout of booster doses at the end of last year.
A fresh campaign is now under way to give a “spring booster” – a fourth dose of vaccine – to people aged 75 and over, residents of older adult care homes, and those aged 12 and over who are immunosuppressed.
Fourth doses of vaccine can be given to people who are at least six months on from their most recent jab.
Figures published last Friday by the ONS showed 4.88 million people in the UK were estimated to have had Covid-19 in the week to April 2, slightly below the all-time high of 4.91 million in the previous week – though infections remained at record levels in both England and Wales.
The number of people in hospital in the UK with coronavirus is similar to the total reached at the start of this year, but is still far below levels seen during the second wave in early 2021 – again reflecting the impact of the rollout of vaccines.
Overall, 191,164 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 1,487 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.