The R rate appears to have fallen from 1.7 to around 1.1 this month based on early results from a study by Imperial College London and Ipsos Mori.
The director of the programme said this could mean efforts to control the virus could be working and that this reinforced the need for protective measures.
Nearly a third of the UK population is under some form of restriction as the government battles to stop the rate of infection from increasing further.
More than 80,000 volunteers were tested in England between September 18-26 as part of the country's largest study into the virus.
The study is examining levels of infection in the general population by testing more than 150,000 participants each month over a two-week period.
Interim results from the fourth report of the study show around 55 people per 10,000 tested positive, which is an increase on 13 people per 10,000 in the previous study.
This implies 411,000 people in England have the virus, meaning over one in 200 people were infected at any one time.
Findings also show that the prevalence of infection was the highest among those aged 18-24, with one in 100 people infected.
Cases increased seven-fold in those aged over 65 from 0.04 per cent to 0.29 per cent compared to the last report.
The north-west of England, which has seen areas such as Burnley and Liverpool placed under local restrictions, had the highest levels of infection.
The number of infections in London increased five-fold from 0.10 per cent to 0.49 per cent.
The final report and findings of all 150,000 volunteers tested between September 18 and October 5 will be published next week.