Data from the Office for National Statistics (ONS), based on analysis of swab tests from more than 23,000 people, found that around 25,000 people in England had Covid-19 at any given time between June 14 and June 27.
This is equivalent to 0.04% of the population, or around one in 2,200 people, the ONS said.
The data looks at infection rates in the community and does not include care homes and hospitals, or other institutions.
The ONS said its estimates suggest the percentage testing positive has decreased over time since the first measurement on April 26 and "this downward trend appears to have now levelled off".
In separate data on just over 3,200 people given an antibody test, around 6% of the population are thought to have antibodies against coronavirus.
This equates to one in 16 or 2.8 million people in England.
In Leeds, a total of 1,908 people have tested positive for Covid-19. Of those people, 333 have died at hospital.