Kings College London (KCL) scientists estimated around 66,033 people were infected every day last week up to October 2, compared with 58,126 the previous week.
Professor Tim Spector, the epidemiologist said the government allowing the virus to “run rampant” with school children was a “real gamble,” and hopes “herd immunity” will start and reduce in children.
If cases do not slow down then face masks may well return to the classroom in the winter, the former Vaccines Minister Nadhim Zahawi said.
Professor Spector said, “While Covid may be less severe in children, allowing Covid to run rampant among them is a real gamble.
“With more than one in 30 older school-children now infected and as we predicted numbers rising, many will not escape long-term symptoms.
“These are the highest rates since January 2021.
“Without vaccination or restrictions in this group, we can only hope that some kind of herd immunity will kick in and cases will drop.”
He added, “The good news this week is our latest research shows having a natural Covid infection before double vaccination means greater protection.
“This is really positive news for overall immunity levels in the UK and means that large numbers of people will have effective and long lasting protection from Covid.
“The evidence supports the need for vaccination, even for those who have already had Covid.
“We need to be less complacent and without restrictions much more focus needs to be put on getting everyone vaccinated before winter to keep up with other countries’ efforts.”