In the week up to 21 November, positivity rates appeared to decrease in the northwest, West Midlands, east of England, London, southeast and southwest, the Office for National Statistics (ONS) said on Thursday.
Over the same period, an estimated 633,000 people in private households in England had Covid-19 – equivalent of around 1.16 per cent of the population.
The figures are slightly down from the previous week, when 664,700 people were estimated to have been infected with the virus.
Overall prevalence of Covid-19 infections fell to 1 in 85 people – down from 1 in 80 the week before.
The ONS said it has been unable to publish a new estimate for the average number of new cases per day of Covid-19 in England, due to issues with data from one of the laboratories that processes swab results.
Its Covid-19 Infection Survey is based on more than 712,000 tests gathered from households across the UK over the last six weeks, regardless of whether people have symptoms.
The figures do not include people staying in hospitals, care homes or other institutional settings.
The ONS reported that infection rates have increased in the East Midlands but have largely appeared to fall elsewhere.
Nonetheless, the highest rates in England continue to still be seen in Yorkshire and the Humber, the northwest and the northeast.
When it comes to age groups, only secondary school age children are seeing a rise in infection rates, while they have dropped in adults aged 35 and over.
Among very young children rates have levelled off, as they have for young adults.
Rates of infection have decreased in Northern Ireland and Wales in recent weeks, the ONS said, but appear to have increased in Scotland in the most recent week.
Ruth Studley, head of analysis for the Covid-19 Infection Survey, said: “At a national level in England, the overall number of infections appears to be levelling off at around one in 85 people who would test positive in the community.”
The ONS study comes as the country prepares to exit the nationwide lockdown on 2 December and move into the regional-based tiered system.
Meanwhile, new data from the government shows that some 60.3 per cent of close contacts of people who tested positive for Covid-19 in England were reached through the Test and Trace system in the week ending 18 November.
This is down slightly from 60.7 per cent in the previous week, and is also just above the all-time low of 59.6 per cent for the week to 14 October.
For cases handled by local health protection teams, 99.0 per cent of contacts were reached and asked to self-isolate. But for cases processed online or by call centres, this figure was 58.8 per cent.
A total of 152,660 people tested positive in England at least once in the week to 18 November, according to the Test and Trace figures. This is the first time since mid-August that the number has fallen week-on-week.