The figure is based on a survey of private households, and is considered by some experts to be the most reliable estimate of infection rates as it does not depend on test uptake and reporting.
The seven day rate of positive cases reported remains higher in Scotland, at 1,860 per 100,000 people, compared to 1,796 in England.
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It comes after the Scottish Government faced pressure to justify restrictions on large events and hospitality when reported case rates were lower in England, which has not introduced similar measures.
Nicola Sturgeon told MSPs on Tuesday that case rates in January had been better than predicted, adding: “There is reason to be optimistic that protective measures, the behavioural response of the general public and the vaccination programme have helped to mitigate, to some extent, the impact of the Omicron wave.”
Case rates have increased in all nations, according to the ONS, with a record high of 4.3 million people in private households across the UK having Covid last week, up from 3.7 million the week before.
It is estimated that one in 20 people in both Wales and Northern Ireland had the virus last week.
Some 297,000 people are thought to have had Covid in Scotland, along with 3.7 million in England, 169,000 in Wales and 99,000 in Northern Ireland.