Children are “very minor players” in the transmission of coronavirus and opening schools would “add little” to the reproduction rate of infection, a leading expert has said.

Professor Russell Viner, president of the Royal College of Paediatrics and Child Health and a member of the Government’s Sage scientific advisory group, told BBC Radio 4’s Today programme on Monday that “reopening schools is one of the least risky things we can do”.

His comments were echoed by Education Secretary Gavin Williamson, who said there was little evidence of transmission in schools.

However, teachers, scientists, opposition politicians and the children’s commissioner for England Anne Longfield have all called for improvements to testing before pupils return.

Prime Minister Boris Johnson has said it is the “national priority” to get children back in class in England next month, but he has been warned by scientific advisers that “trade-offs” may be necessary to keep transmission down.

Ms Longfield welcomed Mr Johnson’s commitment to make children the priority after previously accusing ministers of treating them as “an afterthought”.

But she said regular testing of pupils and teachers, perhaps as frequently as weekly, could be needed even if they do not exhibit symptoms to keep transmission rates down.

Prof Viner said that while children can and do transmit this virus they are “very minor players in the transmission overall”.

He added: “We cannot be in a risk-free society and this is about the risk balance.

“What is the risk balance equation and I think that’s separate for children and young people themselves.

We cannot be in a risk-free society

“It’s very clear for them the benefits and risks, the balance is for them to be back at school.

“For broader society, look, I think it’s also clear that reopening schools is one of the least risky things we can do.

“Anything we do that reopens society will add a small or a larger amount to the overall population reproductive number and for schools we believe that it’s a relatively minor player, it would add little to the overall population R.”

In a statement Mr Williamson said the Government will continue to be guided by the “best scientific and medical advice”.

He added: “The education and care of our children is a national priority.

“We have always been and will continue to be guided by the best scientific and medical advice.

“The latest research which is expected to be published later this year – one of the largest studies on the coronavirus in schools in the world – makes it clear there is little evidence that the virus is transmitted at school.”

But Greater Manchester’s Mayor Andy Burnham said that the Test and Trace programme had to be better to give parents the confidence to send their children back to school.

Speaking on BBC Breakfast on Monday he called on the Government to give more resources to local councils to trace people the national call centres were unable to reach and to also allow people to self-isolate on full pay.

Mr Burnham added: “So many people are struggling to self-isolate because they just can’t afford it.

“We are saying to the Government: you have got to give all employees in the country the ability to self-isolate on full pay, and it’s only that approach that will get Test and Trace system working properly.”

Mr Burnham compared the request to self-isolate to jury service and said people should be supported to do it.

He added: “It’s a simple request we are making, a bit like when you are called up to serve on a jury, when you get a request from the Government to go and be a juror.

“This also is a request from the Government when you’re being asked to self-isolate, so let’s give everybody the ability to follow that request.

“Test and Trace will start working much better if we do that.”

The Association of School and College Leaders said teachers might teach students on a week-on, week-off basis if there was a resurgence of coronavirus and schools were forced to limit the number of pupils attending, with the onus on parents to home-school in the alternate weeks.

The union’s general secretary Geoff Barton said schools were “losing patience” with the Government’s demand to have all children back in school next month while framing no back-up plan if this was not possible.

“If you want to limit the number of children on site or travelling to and from school, a big part of that is using rotas and the obvious way to do it is ‘week on, week off ‘,” Mr Barton told The Daily Telegraph.

It is essential that children get back into school this autumn term.

However, care minister Helen Whately said the Government’s priority was to have children “fully” back at school by September.

She told BBC Breakfast: “Schools are safe and there are extra measures that schools are being advised by Public Health England to take; for instance, to have staggered start and finish times, staggered breaks, to teach children in bubbles, and teachers can enforce, encourage hand washing, hand sanitising, so all the steps that will make schools even safer for our children to be back.”

Asked if schools should stay open in the event of a local lockdown, she said: “Yes, that is the approach, so, for instance, in places like Leicester and Greater Manchester, and areas where we have local restrictions going on, absolutely schools should be still going back. It is essential that children get back into school this autumn term.”

The latest tensions over Covid-19’s impact on education come as a European study suggested reopening schools was not a major danger in community transmission of the disease.

The European Centre for Disease Prevention and Control studied 15 countries, including the UK, and concluded: “There is conflicting published evidence on the impact of school closure/re-opening on community transmission levels, although the evidence from contact tracing in schools, and observational data from a number of EU countries suggest that re-opening schools has not been associated with significant increases in community transmission.”