There has been a 14% rise in people testing positive in the week to 20 September - the biggest increase since the summer.
But there is no clear evidence of an autumn Covid wave starting, says the Office for National Statistics (ONS).
More recent data showing a rise in hospital admissions with Covid has been called "a wake-up call".
Dr Thomas Waite, deputy chief medical officer for England, told BBC News that a number of new sub-variants of Omicron were circulating at low levels, and could be behind the hospital figures.
Daily hospital admissions are lower than where they were for much of July, but highest among the oldest age groups.
However, six out of 10 people with Covid in hospital is being treated for something else - not Covid-19.
"The fact there are people getting so seriously ill they need to go into hospital is a wake-up call to us all that Covid is still here," said Dr Waite.
Health experts have warned of a flu and Covid "twindemic" this winter, urging those who qualify to get their free jabs now.
Although Covid is increasing in England and Wales, the trend is uncertain in Scotland and Northern Ireland, the ONS says.
Sarah Crofts, from the ONS Covid-19 Infection Survey, said: "It is too early to identify whether this is the start of a new wave of infections. We will continue to closely monitor the data."
The ONS estimates are based on thousands of random tests on people in private households across the UK, whether or not they have symptoms.
In the UK as a whole, it is the first time estimated Covid infections have risen above one million since the end of August 2022.
In England, infections rose in the North West, Yorkshire and the Humber, the West Midlands, the East of England, London, and the South East - and in all age groups.
The tests found that about one in 60 people had Covid in the UK in the week to 20 September, up from one in 70 the week before.
But there were noticeable differences in trends in the four nations of the UK.
The ONS says Covid is infecting:
* one in 65 people in England (up from one in 70)
* one in 50 people in Wales (up from one in 75)
* one in 80 in Northern Ireland (the same as the week before)
* one in 45 in Scotland (up from one in 55)
Data is for the week ending 17 September 2022 for England, and the week ending 20 September 2022 for Wales, Northern Ireland and Scotland.
The most common Covid symptom is currently a sore throat, with fever and loss of smell much rarer, according to symptoms logged by 3,000 people testing positive via the Covid symptom app.
Booster jabs against Covid, alongside flu vaccinations, are now being offered to the most vulnerable to help protection over the winter.
Most people will receive a new type of vaccine - made by Pfizer or Moderna - which tackles both the original Covid virus and the recent Omicron variant, offering better protection.
There were 7,000 people in hospital in England with Covid last week - a 37% increase on the week before.
Hospital admissions with Covid were running at around 900 per day, compared to roughly 2,000 in early July during the last surge of Omicron infections.
Hospital patients and care home residents are no longer being tested for Covid in most of the UK, unless they have symptoms.
Dr Mary Ramsay, director of public health programmes at the UK Health Security Agency, is expecting "an unpredictable winter" which will put additional pressure on health services.
"In the coming weeks, we expect a double threat of low immunity and widely circulating flu and Covid-19," she said.
"While Covid-19 and flu can be mild infections for many, we must not forget that they can cause severe illness or even death for those most vulnerable in our communities."
She urged people who were unwell this winter to stay at home and avoid contact with vulnerable people to help prevent infections spreading.