Covid cases are showing "early signs of a potential increase" in England, a respected official study said today.
The Office for National Statistics estimated around 1 in 1,110 people in the community had the virus at any time in the week to May 15.
That compared to around 1 in 1,340 people a week earlier.
There was a slight upward tick in three regions - the North East, Yorkshire and The Humber and the South East.
By comparison the ONS said the percentage of people testing positive in Wales remained low, and it continued to fall in Scotland.
Because cases are low, however, there is also a wide margin for error.
Today's study estimated the number of weekly cases in England's community at between 38,800 and 60,300. A week earlier, the estimate was between 31,900 and 50,900.
It comes after a spike in UK cases of the B.1.617.2 variant of Covid, originally found in India.
Latest data shows there have been 3,424 cases of the Indian strain in total in the UK, up 2,111 on the week before.
49 cases have also been found of a new variant AV.1, which is said to have three mutations that could be of concern.
The prevalence of Covid is still far lower than in the second peak earlier this year - when as many as 1 in 30 people in London had the virus at any one time.
The weekly ONS infection survey models the number of cases taking into account that not everyone with Covid will get a test.
It only covers the "community" and not institutional settings such as hospitals, care homes and prisons.
Today's survey said: "In the week ending 15 May 2021, there were early signs of an increase in the percentage of people testing positive in the North East, Yorkshire and The Humber and the South East.
"The trend was uncertain for all other regions in the same week.
"In many regions positivity rates are very low so trends will be difficult to identify since they are affected by small changes in the number of people testing positive from week to week."
The study also cautioned: "In the data used to produce these estimates, the number of people sampled in each region who tested positive for the coronavirus (COVID-19) was low relative to England overall.
"This means there is a higher degree of uncertainty in the regional estimates for this period, as indicated by larger credible intervals."
Boris Johnson today insisted he was still currently on track to ease legal restrictions on gatherings - which are still limited to six people indoors - from June 21 at the earliest.
The Prime Minister is due to receive more data next week on how transmissible the Indian strain is - and therefore whether it might have to delay the end of lockdown rules.
He told reporters today: “We will let people know as much as we possibly can by the end of the month, about weddings for instance, all the details we’ll try and let people know by the end of the month exactly where we think we will be on June 21 - step 4.
“At the moment I can’t see anything that makes me think we’re going to have to deviate from the roadmap - though clearly we must remain cautious in our approach.”
Some voluntary guidance or rules like masks on public transport could remain even beyond June 21.
A minister, Robert Buckland, suggested people might choose to wear masks past the end of the pandemic to stop spreading ailments like the common cold.
