Ministers should be planning for a huge rise in Covid cases as schools return, the government’s scientific advisers have warned, as debate continues over whether all older children should be offered a Covid vaccine.

A document released on Friday revealed that scientists on the modelling group of the Scientific Advisory Group for Emergencies (Sage) have issued a fresh alarm about the impact of schools reopening in encouraging the spread of infections.

“It is highly likely that high prevalence will be seen within schools by the end of September 2021,” the group predicts in the document.

“This may reflect either community or within-school transmission, and the role of schools in driving wider transmission remains uncertain. Regardless of this, it would be sensible for government to plan for this eventuality.”

Concerns have been growing around the return of pupils to school in England, Wales and Northern Ireland after a dramatic uptick in cases seen in Scotland since schools reopened there.

With the rise in Scotland having begun before the start of the new term, experts have suggested that changes in Covid restrictions and factors related to the end of the school holidays – such as adults returning to work – may have played an important role, although mixing in schools may have contributed.

According to the new document, dated 11 August, many school-age children will not have protection against Covid: by mid-May this year only 20% of schoolchildren were thought to have immunity through infection. In addition, at present few children under the age of 16 are eligible for vaccination.

“Schools will represent a high proportion of remaining susceptible individuals and it is highly likely that exponential increases will be seen in school-attending age groups after schools open. Vaccination will also have made almost no difference in these population groups over the summer holidays,” the group write.

The Sage members warned that when schools in England reopen from next week, “the mitigations in place to limit transmission within schools will be much reduced compared to the spring and summer terms. Additionally, the prevalence of infection in the community and school-age groups will be higher than in May 2021.”

Since the end of the last school year the government in England abandoned most preventive measures, such as mask wearing in secondary schools, social distancing and the use of smaller groups known as bubbles to contain the spread of infection. It has also dropped the requirement for close contacts of confirmed cases to self-isolate.

Kevin Courtney, joint general secretary of the National Education Union, said the Sage commentary was a “rebuke” to Gavin Williamson as education secretary.

“Next to nothing has been done to prepare for the possibility of large numbers of cases which will lead to lots of education disruption as children and staff have to isolate because they are positive,” said Courtney.

The NEU wants the government to support schools taking additional measures such as face coverings and social distancing from the start of term.

“The danger is not that schools and colleges will be slow to act but that government is,” Courtney said.

Modelling published in the Sage document suggests the level of immunity among secondary school-age pupils when schools return is important – should this be at 60% or 70% by the time schools return, R may remain below 1, but at 40% or 50% R may exceed 1, meaning exponential growth and outbreaks of school epidemics.

While the group said that school transmission could be reduced by twice-weekly testing, it stressed that a rise in infections could be highly disruptive for teachers and students because of missed learning, as well as “consequences for parents and carers, and the wider workforce implications”.

A survey by the Teacher Tapp community showed that at least a third of secondary schools in England are delaying the start of teaching to conduct Covid tests on their pupils. The survey of 4,000 teachers and school leaders in England found that while most delays would be for one or two days, nearly one in 10 schools will delay teaching for three or more days to carry out tests.

Department for Education guidance says that secondary schools and colleges may stagger the return of pupils across the first week to manage the testing process.

Geoff Barton, general secretary of the Association of School and College Leaders, said: “It is extremely frustrating that the government has failed to provide schools and colleges with sufficient support to deliver this huge logistical exercise and once again left them to shoulder what is essentially a public health responsibility.”

Another Teacher Tapp survey also found that the vast majority of teachers rated the Covid guidance given to schools for the new term as “poor” or “terrible”. None of the teachers rated it as “excellent”.

Last term the government’s weekly attendance figures showed hundreds of thousands of pupils were kept out of school for Covid-related reasons. That culminated in a million children missing school in the second week of July, including more than 770,000 self-isolating for being in close contact with a confirmed infection while at school.

The new rules mean self-isolation will now not be required. The DfE is to stop publishing the Covid absence figures on a weekly basis, and will instead publish “a fortnightly summary” starting from 21 September.

James Bowen, director of policy at the National Association of Head Teachers, said there “seems to be no clear justification or rationale” for the change. The DfE said the decision was made by its chief statistician and reflected “user need”.