Infections increased by 50% between 3 May and 7 June coinciding with the rise of the Delta variant, which has become dominant in the UK since first being detected in India.
Delta has overtaken the Alpha (Kent) variant, and now accounts for up to 90% of coronavirus cases.
The number of COVID-19 cases is doubling every 11 days, according to data from the REACT-1 study by scientists at Imperial College London, who said their findings showed a “rapid switch” from the Alpha variant to Delta.
The figures also show that one in 670 people was infected, with the highest prevalence in the North West.
Stephen Riley, professor of infectious disease dynamics at Imperial and one of the study authors, said the exponential increase in prevalence is being driven by infections among younger people.
The REACT-1 study showed prevalence is highest among those aged five to 12, as well as younger adults aged 18 to 24.
Infections in these age groups are about five times higher than in those aged over 65, who are mostly fully vaccinated.
Commenting on the findings, Prof Riley said: “The key thing to point out here is that we are in a very different part of the epidemic in the UK and it is very difficult to predict the duration of the exponential phase.
“Last autumn and last spring… when we started to observe exponential growth – in some ways it was much more alarming because we knew there was very, very little immunity in the population.
“(But now) because of the vaccination (programme), we know there is a lot of immunity in the population.
“Even though there is a lot of immunity, it does not prevent some exponential growth and that is what we are seeing here.”
The scientists said the expansion of the vaccination programme “should help substantially to reduce the overall growth of the epidemic”.
Those aged 21 and 22 became eligible for the vaccine on Wednesday and the expectation that those aged between 18 and 20 will follow by the end of the week.
Study author Paul Elliott, director of the REACT programme and chair in epidemiology and public health medicine at Imperial, said: “I think we can take quite a lot of comfort from the fact that when we look in the details, it does appear that there is very, very good protection in the older ages, where there is virtually everyone double vaccinated.
“And in the younger group under the age of 65, where a much smaller proportion have been vaccinated or double vaccinated, most infections are occurring in the unvaccinated group.
“And the government has clearly announced that they want to vaccinate all adults in the period between now and 19 July, I think that will make a very big difference and increase the total amount of population immunity.”
Data showed that the link between infection rates and hospital admissions remained weak for those aged 65 and older, but converged for those under that age.
Prof Riley said: “These patterns are consistent with two vaccine doses being highly effective.”
He added: “We expect the rapid rollout into those ages, especially first doses for people who have not had any dose, and then secondary says for those who’ve had one dose, should effectively slow that growth, even against all the other factors.”