Total Covid-19 infections in the UK have risen 31%, the biggest percentage jump since June, with most of the country now seeing a steady increase in virus levels.

There has also been “another notable rise” in infections among older age groups who are seeing the highest rates of admission to hospital.

The figures come on the day that everyone in England aged 50 and over can now book an appointment to receive a fresh booster dose of coronavirus vaccine.

Some 1.7 million people in private households across the UK are likely to have tested positive for coronavirus in the period September 23 to October 3, according to the Office for National Statistics (ONS).

This is up from 1.3 million in the previous survey, which covered the period September 18 to 26.

It is the highest UK-wide total since late July but is still below the 3.8 million weekly infections in early July, at the peak of the wave caused by the Omicron BA.4/BA.5 subvariants of the virus.

There is a lag in the reporting of the ONS data due to the time it takes for the survey to be compiled.

More recent figures show the number of people in hospital testing positive for Covid-19 is still on a clear upwards trend, though there are signs the rate of increase may have slowed in recent days.

Sarah Crofts, ONS deputy director for the Covid-19 infection survey, said: “Infections have risen again across much of the United Kingdom, continuing the pattern of steady increases seen over recent weeks, although Scotland and the north-east of England had uncertain trends in the latest week.

“We have also seen another notable rise in infections amongst older age groups in England and Wales, underlining once again the need for close monitoring as we move through the colder months.”

In England, the number of people testing positive for coronavirus in the latest survey was 1.5 million, or around one in 35 people – up from 1.1 million, or one in 50, in the previous survey.

Wales has also seen a rise, where the latest estimate for infections is 74,900, or one in 40 people, up from 63,400, or one in 50.

The trend in Scotland is described by the ONS as “uncertain”, with 109,700 people likely to have Covid-19 in the latest survey, or one in 50, compared with 113,000 in the previous survey, or one in 45.

In Northern Ireland the latest estimate is 45,100 infections, or one in 40 people, compared with 46,100, which is also one in 40 – though the longer trend here is showing an increase.

Infection rates in England are highest among people aged 70 and over, with 3.7% likely to have tested positive for coronavirus in the latest survey, or around one in 25, the ONS said.

This is up from 2.5%, or one in 40, in the previous survey.

Rates are lowest among children from school Year 7 to 11, at 1.5% or one in 70.

All regions of England have seen a rise in the percentage of people testing positive except for the north east, where the trend is uncertain.

Covid-19 patient levels are continuing to increase with 10,608 people in hospital in England as of 8am on October 12, NHS data shows.

This is up 10% from 9,631 a week earlier and is the highest figure since the end of July.

Patient numbers topped 14,000 in mid-July at the peak of the BA.4/BA.5 wave, then fell steadily until mid-September, since when they have been on the rise.

However, the rate of increase has slowed in recent days.

The jump of 10% in the seven days to October 12 is much lower than the rise of 37% in the seven days to October 5.

Patient numbers are on an upwards trend in both Scotland and Wales, while in Northern Ireland they have levelled off after a small rise.

Around two-thirds of patients in hospital who test positive for Covid-19 are being treated primarily for something else.

But they need to be isolated from patients who do not have the virus, putting extra pressure on staff already struggling to clear a record backlog of treatment.

Hospital admission rates are highest among over-85s, at 151.7 per 100,000 people in the week to October 9.

This is up from 130.3 in the previous week and is the highest rate for this age group since mid-July.

Dr Mary Ramsay, director of public health programmes at the UK Health Security Agency (UKHSA), said: “We’re seeing sustained increases in Covid-19 cases and hospitalisation rates, so we continue to urge those eligible for vaccinations to come forward, whether that’s a first dose or a booster.

“Vaccines are the best protection against severe disease and hospitalisation this winter and it’s never too late to take up your first dose.

“If you are unwell or have symptoms of a respiratory infection, it is particularly important to avoid contact with elderly people or those who are more likely to have severe disease because of their ongoing health conditions.”

More than half (51.1%) of people aged 80 and over in England are now likely to have received an autumn booster dose of Covid-19 vaccine, along with a similar proportion (52.1%) of 75 to 79-year-olds.

The booster is intended to increase protection against serious illness during new waves of the virus.

The UKHSA data, which covers vaccinations up to October 9, also shows that 45.9% of 70 to 74-year-olds are estimated to have had the booster, as well as 37.7% of people aged 65 to 69.

All people aged 50 and over in England, Wales and Northern Ireland are now able to book an appointment for the booster, providing they had their last jab at least three months ago.

People aged 50 to 64 in Scotland will be invited soon.

Doses are also available to frontline health and care workers, pregnant women and people with weakened immune systems.