Cases of coronavirus were rising exponentially among five to 17-year-olds in September, coinciding with the start of the autumn school term in England.
The findings from the React-1 study also support the need for vaccine boosters, with a higher prevalence of double jabbed people testing positive within three to six months of their vaccination.
It came after the latest Office for National Statistics (ONS) figures showed that around one in 15 children in school years seven to 11 in England are estimated to have had coronavirus in the week to October 2.
Dr Jenny Harries, chief executive of the UK Health Security Agency, said: "These data demonstrate that while our vaccination programme continues to make a huge difference, the pandemic is not over".
Listen to our coronavirus podcast:
The study, conducted by Imperial College London and Ipsos Mori between September 9 and September 27, suggests one in 120 people were infected, although the prevalence appears to be remaining stable overall.
According to the data, the infection rate is growing among those aged under 18, or school-age young people, and falling among those aged 18-54.
However, relatively few schoolchildren aged five to 17 have been vaccinated in the UK, though single doses are now being offered to those aged 12 years and over.
Earlier this week, ministers urged parents to get their children vaccinated against Covid-19 amid concerns about the vaccination programme in secondary schools.
Researchers say it is important the vaccination programme maintains high coverage and reaches children and unvaccinated, or partially vaccinated adults, to reduce transmission and associated disruptions to work and education.
Provisional data from the government’s coronavirus dashboard suggests that 11.7% of 12- to 15-year-olds in England have been vaccinated as of October 10, compared to 38.9% of 12- to 15-year-olds in Scotland.
According to the React study, overall vaccine effectiveness against infection was estimated to be around 63%-66%.
More than 100,000 volunteers took part in the study to examine the levels of Covid-19 in the general population.
The latest data show that prevalence of the virus in the population in England has increased to 0.83%.
Among households with one or more children, prevalence was also higher at 1.37% compared with 0.40% in households without children.
Professor Paul Elliott, director of the React programme from Imperial’s School of Public Health, said: “Our latest data show that infections are high and rising in school-aged children.
"Households with children also had a higher prevalence of infection, suggesting that children may be passing on the virus to those that they live with.
"These trends reinforce how important it is for children aged 12 and above to get vaccinated and help curb the spread of infection, and minimise disruption to education."