However, the trend in some parts of the country is uncertain, with increased numbers in Scotland.
This is down 7% on the previous week and is the lowest UK-wide total since the week to September 25 2021, when the number stood at 837,800.
The overall number of infections has been on a downwards path since early July, when the total hit 3.8 million at the peak of the wave caused by the Omicron BA.4 and BA.5 subvariants of the virus.
The 7% drop in the latest figures is the smallest week-on-week percentage fall since the current decline began, however.
There are also contrasting trends among UK nations and regions.
In England, the percentage of people testing positive for coronavirus in the week to September 5 was 705,800, or around one in 75 – down from 770,800, or one in 70, in the seven days to August 28.
But in Scotland, 113,500 people were likely to have tested positive for Covid-19 in the latest week, or one in 45 – up from 104,400, or one in 50.
Trends in both Wales and Northern Ireland were described by the ONS as “uncertain”.
The latest estimate for infections in Wales is 28,200 people, or one in 110, compared with 31,500 in the previous week, or one in 95.
And in Northern Ireland the estimate is 33,700, or one in 55 people, compared with 38,000, or one in 50.
Infections are estimated to have fallen in London and south-east England, while in all other regions the trend is uncertain.
Among age groups in England, the percentage of people testing positive is estimated to have increased for children from age two to school year six.
All other groups have seen a decrease, except those from school year 12 to age 34, where the trends were again described as uncertain.