A quarter of a million children in England missed school last week because of Covid infections, self-isolation or school closures, making it the most disrupted week since schools fully reopened in March and prompting calls for pupils to be vaccinated.

The upsurge has been most marked in northern centres such as Oldham, where Covid-related absences in schools are more than double the national rate. Andy Burnham, the mayor of Greater Manchester, said that self-isolation rules for children needed to be reformed to avoid further disruption to their education.

The national figures from the Department for Education (DfE) showed that one child in every 30 at state school was out of the classroom on 17 June, including 9,000 pupils with confirmed Covid-19 cases, 16,000 with suspected cases and more than 7,000 whose schools had shut entirely because of Covid outbreaks.

The majority of absences came after contact with suspected or confirmed cases within schools, with 172,000 students self-isolating last week, compared with 40,000 the week before. Just 42,000 were self-isolating because of contacts outside their school.

Burnham called for a “more proportionate” handling of self-isolation: “Obviously if people are testing positive, then that is an issue that needs to be dealt with. But when it comes to the contacts of those kids, then maybe there are other arrangements that can be looked at.”

Gerard Jones, managing director of children and young people for Oldham council, backed daily testing for children rather than self-isolation, saying that the surge in absences would be treated with more alarm if it happened in London. “If you were in our communities and you saw the level of impact, you know you might feel a bit differently about it,” Jones said.

Currently 3,500 children and more than 200 school staff are self-isolating in Oldham, with more than 1,500 children sent home from school since Friday. The number of cases per 100,000 people is 207, compared with the UK rate of 89 per 100,000, with the highest rates among younger, unvaccinated age groups.

Jones argued for vaccines to be given to students 12 years and older, likening it to public health programmes that give flu jabs in schools to protect vulnerable and elderly people. “It’s only when we vaccinate the school population that we actually will get to a viable long term plan [to live with Covid],” Jones said.

School leaders said that the disruption was a warning that the spread of the Delta variant within schools posed further dangers, with head teachers “hanging on” until the end of the school year next month.

Mary Bousted, joint general secretary of the National Education Union, warned that absences and school closures could “rapidly return to the unwelcome peaks” seen last year.

“We are now seeing the effect of the spreading Delta variant on national figures, and absences from school are only likely to continue rising in the coming weeks, along with obvious disruption to pupils’ education,” Bousted said.

Geoff Barton, general secretary of the Association of School and College Leaders, said: “Schools have no choice other than to hang on until the end of term endeavouring to manage this situation, and we can only pay tribute to them for everything they are doing in these extraordinarily difficult circumstances.

“However, the government must think urgently about how to reduce educational disruption in the next academic year after the summer holidays.

“We simply cannot have another term of large numbers of children spending time out of school because of coronavirus.”

The DfE figures showed that Covid-related absences have more than doubled in primary schools, rising to 2.7% from 1.1% in a week, while secondary school absences trebled from 1.4% on 10 June to 4.2% last week.

Covid is also affecting a small but rising number of teachers and teaching assistants, with nearly 1% of teachers having to self-isolate, compared with 0.2% the previous week. The proportion of teachers with confirmed infections was 0.2%.