They were up slightly in England and Northern Ireland but not in Scotland and Wales, according to the Office for National Statistics (ONS).
In the week to 26 November, about 1.1 million people in the UK tested positive - 1.7% of the population.
Covid levels had been falling since mid-October and remain low even now.
Those who are eligible are being urged to get a Covid booster jab this weekend before families mix over the holiday season.
NHS England director of vaccinations and screening, Steve Russell, said: "If you are yet to have your Covid booster or flu jab, please book in as soon as possible and take up the opportunities on offer around the country this weekend to ensure you have maximum protection over Christmas."
Pop-up vaccination sites will be located at some community health centres, food banks and places of worship, NHS England says.
Michelle Bowen, from the ONS, said: "Infections have continued to increase across England, increased in Northern Ireland for the first time in a month and the trend in all other UK countries is now uncertain.
"Across English regions and ages, it is a mixed picture of uncertainty and increases in infection rates, and we will continue to monitor the data carefully over the winter months."
The ONS estimates are based on tests for Covid-19 on thousands of people in private households across the UK, but not in hospitals or care homes.
The results show that infections went up in London, south-east England, Yorkshire and the Humber and the east of England, and were highest in secondary-age children and people in their early 20s.
But the ONS says there is uncertainty around the figures because fewer than normal test results were received due to postal strikes.
The latest estimates by UK nation are:
* one in 60 people infected in England
* one in 60 in Scotland
* one in 70 in Wales
* one in 50 in Northern Ireland
Official government figures show a slight rise in the number of people admitted to hospital with Covid and of patients in hospital with Covid.
Anyone who is over 50, a health or social-care worker, carer or who has a condition that makes them particularly vulnerable to Covid can have a booster jab.
So far, 16.5 million people have had the latest Covid booster.