Data from the ONS reveals an estimated 28,300 people in England had the virus in the community during the week ending 9 August.
This is equivalent to 1 in 1,900 indviduals being infected. During the latest week, the ONS said there were around 0.69 infections for every 10,000 people in England.
This is equivalent to 3,800 new infections everyday.
The news that infections are not rising will be a relief to ministers ahead of plans for further easing of lockdown restrictions this weekend.
Beauty salons and other close-contact services, soft play areas, casinos and indoor performance venues will be able to reopen after plans were delayed following a spike in cases last month.
According to the ONS the results of its infection survey showed "some evidence of a small increase in the percentage of people testing positive for Covid-19 in July, following a low point in June" but it said the increase in cases had not continued.
Daily testing has shown an increase in positive cases with two consecutive days earlier this week of more than 1,000 people testing positive. Officials within the government's test and trace service believe the increase in positives is due to more testing in hot spot areas and a rise in people seeking tests when they are unwell.
Katherine Kent, co-head of the Covid-19 infection survey said: “This week’s estimate suggests that the increase in infections in England seen in July has now levelled off.
“Regional analysis of antibody data for England, published for the first time this week, show that a higher percentage of people in London have ever tested positive for antibodies to the virus than in Yorkshire and the Humber, the East Midlands, the South East and the South West, though there is not yet enough evidence to show differences between other regions of England.”