The new figures come as the latest round of Covid booster vaccinations gets under way, with residents in care homes for the elderly among the first to receive their shots this week.
The introduction has been brought forward as protection against the latest Omicron subvariant of Covid-19, BA.2.86, which was first identified in the UK on August 18.
But it is still too early to assess the effects of the new strain, with scientists saying they need more data before drawing “firm conclusions”.
Hospital admissions of patients who tested positive for Covid-19 stood at 4.6 for every 100,000 people in the week to September 10, up from 3.7 for every 100,000 the previous week and the highest since the week ending April 30, according to the UK Health Security Agency.
This is still some way to go before the level reached at Christmas 2022, when the rate stood at 11.8 for every 100,000, and it is also well below the figures during the first year of the pandemic.
But the rate has been on a clear upwards trend for the past two months.
Rates remain highest among people aged 85 and over, at 51.1 for every 100,000, and those aged between 75 and 84, at 21.2.
Covid-19 booster jabs will be offered to everyone in the UK aged 65 and over in the next few weeks.
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The number of people in hospital in England who have tested positive for the virus is also continuing to rise, at 3,356 as of September 10, up 15 per cent week on week from 2,915, and the highest since May 19.
The total reached nearly 10,000 during last winter and more than 30,000 in the winter of 2020-2021.
Not enough data has been collected around the world to make a reliable assessment of how BA.2.86 might be spreading, the UK health authority said.
Only 37 cases of BA.2.86 in England have been identified in laboratories so far, 28 of which have been linked to an outbreak in a care home in Norfolk at the end of August.
Seven of the 37 were admitted to hospital and no deaths from Covid-19 have been reported.
Another five BA.2.86 cases have been identified in Scotland, while there have been no cases detected in Wales or Northern Ireland.
Dr Renu Bindra, UKHSA incident director, said that while BA.2.86 has a “significant number of mutations” compared with other variants circulating, the data so far is “too limited to draw firm conclusions” about the impact this will have on the severity of the virus.
“It is clear that there is some degree of widespread community transmission, both in the UK and globally, and we are working to ascertain the full extent of this," Dr Bindra said.
“In the meantime, it remains vital that all those eligible come forward to receive their autumn vaccine as soon as it is offered to them.”
There are no longer any official estimates of the prevalence of Covid-19 among the UK population, meaning it is impossible to get a full and reliable picture of its spread.
Testing for Covid-19 has also been scaled back sharply, so there is not as much data available.
In the absence of more comprehensive figures, the number of people in hospital with coronavirus can offer a guide to changes in the level of Covid-19 in circulation.