Last week’s estimate was 17,200 new infections per day and the week before 12,600.
The total number of people suspected of being infected in England has also increased dramatically, from 224,400 to 336,500 in one week.
This works out to about 1 in 160 people, compared to 1 in 240.
The figures – October 2-8 – are for private households and do not include people living in hospitals and nursing homes.
“The estimate shows that the number of infections has continued to rise rapidly in recent weeks,” the Bureau of National Statistics said.
He said there was also “clear evidence” of regional variations.
Places with tighter lockdowns – like the North West, North East and Yorkshire – have seen significantly higher infection rates than areas such as the south and east of England.
But trends show “growth in positivity in all parts of England”, ONS added
Older adolescents and young adults were the most infected.
“Smaller increases are also apparent in all other age groups, with the exception of people aged 70 and over,” the research said.
The ONS Infection Survey performs its own tests on tens of thousands of people every week, whether or not they show symptoms of coronavirus.
In Wales there could be some encouraging signs.
The researchers said there was “evidence that the positivity rates have now stabilized, although the uncertainty is high.”
Some 7,900 people there are estimated to be infected with the virus during the week in question – or 1 in 390 people.
This compares to 6,100 and 1 in 500 the week before.
Northern Ireland’s estimate has doubled, however, to around 1 in 250 people infected from 1 in 500.
Its figures cover a longer period, from September 25 to October 8.
Scotland is not covered by the survey.