That compares to a record high of one in 11 that was seen in Scotland in the week to Sunday March 20, as the BA2 Omicron variant saw cases surge.
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The ONS said the percentage of Scots with the virus had decreased in the week ending April 3.
Its latest report estimates 396,800 people, or 7.54% of the population, in Scotland had Covid that week, equating to around one in 13 people.
Sarah Crofts, head of analytical outputs for the Covid-19 infection survey at the ONS, said: “While infections remain high, there are early signs in our latest data that they may no longer be increasing in some parts of the UK.
“Across English regions, there is a mixed picture in trends and we have seen a welcome decrease in Scotland.
“However, rates in Wales continue to rise and the trend in Northern Ireland is uncertain.
“It is too early to say if infections have peaked in England and Scotland. We will continue to monitor the data closely.”
Meanwhile, the latest daily figures from the Scottish Government show another 35 Covid deaths and 6,215 more cases of the virus were recorded in the past 24 hours.
It takes the total number of people who have died within 28 days of testing positive for Covid to 11,650.
Statistics show there were 2,252 people in hospital on Thursday with recently confirmed coronavirus, down from 2,304 the previous day.
The hospital total includes 23 people in intensive care, which is down from 27 on Wednesday.
A total of 4,369,103 people have now received their first dose of Covid vaccine, 4,097,075 have had a second jab, and 3,457,690 have had a third dose or booster.