Levels of positive tests are rising in London and could be on the up in the east of England, according to data from the Office for National Statistics.
Figures for the week to 5 December, as England’s second lockdown was ending, suggest infection levels continued to fall in other regions.
Infection rates are still highest in secondary school-age children, the ONS says.
Across the UK, the picture is mixed with Wales seeing rising infections.
In Northern Ireland, the percentage of people testing positive continues to fall – while in Scotland it has stayed the same.
The ONS figures are one source of data used by the government’s scientific advisers to judge the spread of the virus and take decisions on restrictions on people’s daily lives.
They are based on swab tests of thousands of people in households whether they have symptoms or not. The estimates are thought to give a more accurate picture of how many people are infected with the virus than data on positive tests alone.