A total of 722.9 new cases per 100,000 people aged five to nine were recorded in the seven days to November 14, up week-on-week from 484.5.
The rate for 10 to 19-year-olds is 694.2, up from 571.7.
The figures, from the UK Health Security Agency (HSA), are likely to reflect the return of pupils to school after the half-term holiday in late October.
Case rates have also jumped for all age groups between 20 and 59, though the week-on-week increase is smaller.
Rates have fallen in age groups for people aged 60 and over.
Across England, rates have increased in all regions except the north-east.
South-west England has the highest rate, at 485.3 cases per 100,000 people, up from 415.5.
London has the lowest rate at 275.2, up from 234.7.
The rate of Covid-19 hospital admissions in England stood at 7.6 per 100,000 people in the week to November 14, unchanged from the previous week.
Admission rates continue to be highest among people aged 85 and over, at 40.1 per 100,000.
Responding to the figures, Professor Steven Riley, HSA director-general of data, analytics and surveillance, said: “Rates of Covid-19 continue to increase in those from younger age groups, and hospitalisations remain highest in those aged 85 and over.
“More people than ever are eligible for second and booster doses and it is as important as ever to get vaccinated or receive a booster jab as soon as you are offered one.
“Socialising indoors in places with poor ventilation increases the risk of infection. Help protect yourself and loved ones by opening windows and doors to ventilate the room when meeting people inside. Wash your hands regularly and wear a mask in crowded places. If you have any Covid-19 symptoms, stay at home and get a PCR test as soon as possible.”
Meanwhile, a total of 46,807 new cases of Covid-19 in the UK were reported by the Government on Thursday – the highest number for a single day since October 22.
The seven-day average of new cases currently stands at 39,609, up from 34,600 a week ago.
This is below the level seen during much of October, however.