The figures are down from one in 70 the previous week, according to the Office for National Statistics.
One in 80 is the equivalent of about 697,100 people.
At the peak of the second wave in early January, around one in 50 people in England were estimated to have coronavirus.
Meanwhile, a total of 2,542 deaths occurred in England up to September 12 of people who were either confirmed or likely to have had the Delta variant of Covid-19 and who died within 28 days of a positive test, according to new figures from Public Health England.
Of this number, 204 were under the age of 50 and 2,336 were aged 50 or over.
Of the 204 deaths of people under 50, 132 (65%) were unvaccinated, 17 (8%) had received one dose of vaccine and 48 (24%) had received both doses.
Of the 2,336 deaths of people aged 50 or over, 590 (25%) were unvaccinated, 149 (6%) had received one dose of vaccine and 1,565 (67%) had received both doses.
A small number of virus samples could not be matched with vaccination records.
It came as the Environment Secretary said a Cabinet sub-committee meeting due to take place on Friday could sign off on travel rule changes.
The green and amber lists are expected to be merged to form one category of low-risk countries while the number of destinations on the red list will be reduced.
There is also speculation that fully-vaccinated arrivals will no longer need to take a pre-departure lateral flow test or a post-arrival PCR test.
George Eustice told Sky News: “My understanding is that no decisions have actually been taken yet, although I understand there may be a meeting today to review this. We regularly review those travel restrictions.
“Obviously we took an important step earlier this summer when we removed the need to quarantine for those countries coming from amber list countries – that was a really big step forward – but we have retained the need for testing, and that’s really so we can pick up any variants of concern through that PCR test.
“But, look, I know this has been raised by the travel industry, that they think some of that testing may be unnecessary, may be onerous – the Government will be listening to that and the Covid sub-committee of Cabinet that decide these things will be considering that probably later today.”
Additional reporting by PA Media.Internet Explorer Channel Network