The Office for National Statistics says a total of 215 coronavirus-related deaths were registered in the week to 25 September.
In the week before, there were 139 COVID-19-related deaths registered, and before that it was 99.
COVID-19 accounts for 2.2% of all deaths in England and Wales, according to the ONS.
It means that more than 58,000 coronavirus-related deaths have been registered in the UK, according to data from the statistics agencies.
Up until 25 September, 52,943 people had died with COVID-19 in England and Wales, while figures in Scotland show that there had been 4,257 coronavirus-related deaths there.
Some 901 deaths had been recorded in Northern Ireland, according to the Northern Ireland Statistics and Research Agency.
The data includes death certificates where COVID-19 had been mentioned and includes suspected cases.
Registered deaths involving COVID-19 increased in every English region, except the East Midlands, where the weekly total fell from 14 to 11.
Across the rest of England:
- North West - 60 deaths (up 21 on the last week)
- West Midlands - 33 deaths (up 18)
- Yorkshire and the Humber - 29 deaths (up eight)
- London - 23 deaths (up 10)
- South East - 16 deaths (up five)
- North East - 13 deaths (up five)
- East - 10 deaths (up two)
- South West - eight deaths (up three)
In Wales, deaths increased by seven to 12.
In total, there were 9,634 deaths registered in England and Wales in the week ending 25 September, which was 111 more than the previous week and 2.7% higher than the five-year average.
Figures from the ONS are different to those provided by the the Department of Health and Social Care, which says that up until 5 October, 42,369 people had died within 28 days of having a positive coronavirus test.
On Monday, more than 12,500 new COVID-19 cases were reported by the government - one of the highest announcements since the beginning of the pandemic.
However, an earlier mistake in collating the data using Microsoft Excel meant that almost 16,000 cases were delayed being put into the official system.
ANALYSIS: By Ashish Joshi, health correspondent
The five year average is seen by many as the best indicator of how COVID-19 is impacting on the country's health. It compares the number of people who would normally have died at this time of year with the number of deaths actually reported.
Deaths in hospitals and care homes were below the five-year average, while deaths in private homes remained above, with 749 more deaths than would typically be expected.
There has been some concern about the number of people dying in their homes and a few explanations have been put forward as a possible explanation. It is believed some of these people are terminally ill patients who have been discharged from hospital to make bed space available during the pandemic.
It is also thought that these deaths could be an indirect result of COVID-19. Almost all non-urgent operations were paused during the peak of the pandemic and hospitals are now trying to restore elective procedures.
These figures might also be showing the impact of a failure to get medical help.
Doctors have consistently voiced fears about missing patients who suspect they may have an illness and refuse to seek treatment through their doctor's surgery or by attending hospital.
This could be because they are either afraid of attending clinics where they think they may come into contact with COVID-19 or because they feel they do not want to put a burden on the NHS at such a critical time.