One in 70 is the equivalent of about 786,300 people.
At the peak of the second wave in early January, around one in 50 were estimated to have coronavirus.
The percentage of people testing positive for Covid-19 is estimated to have increased in all regions of England, except the East of England where the trend is uncertain, the Office for National Statistics said.
Yorkshire and the Humber and East Midlands regions had the highest proportion of people of any region likely to test positive for coronavirus in the week to October 2, at around one in 55.
London and eastern England had the lowest at around one in 90.
In Wales, around one in 55 people is estimated to have had Covid-19 in the week to October 2, unchanged from the previous week and still the highest since the week to December 23 2020.
In Northern Ireland, the latest estimate is one in 130, down from one in 65 the previous week.
For Scotland, the ONS estimates around one in 60 people had Covid-19 in the week to October 2, down from one in 55 the previous week.
All figures are for people in private households.
When modelling the level of Covid-19 infections among different age ranges in England, the ONS said rates have increased for those in school years 7 to 11, people aged 35 to 49 and those aged 70 and over.
The percentage testing positive decreased for those in school year 12 to age 24, while the trend was uncertain for those aged two to school year 6, people aged 25 to 34 and those aged 50 to 69.
Around one in 15 children in school years 7 to 11 are estimated to have had Covid-19 in the week to October 2 - the highest positivity rate for any age group.
Meanwhile, England’s weekly Covid-19 R number was estimated on Friday at between 0.9 and 1.1.
A reproduction number between 0.9 and 1.1 means that for every 10 people infected, they will on average infect between 9 and 11 other people. Last week the R number was estimated between 0.8 and 1.1.