Boris Johnson has said getting all children back to school full-time in England next month is the “right thing for everybody” amid calls to boost coronavirus testing and tracing to ensure a safe return.

The Prime Minister reiterated his pledge to reopen schools to children across the country in September as he insisted that they were “safe” and “Covid secure”.

His comments come after teachers, scientists, opposition politicians and the children’s commissioner for England Anne Longfield have all called for improvements to testing before pupils return in September.

One school leaders’ union said the Government should have a plan B in place for schools – such as a “week-on, week-off” rota system for pupils – if there are further lockdowns and spikes in Covid-19 cases.

But speaking to reporters at a school in east London, Mr Johnson said he hoped schools would not be forced to close as a result of local action, adding it is the “last thing” that the Government wants to do.

The last thing we want to do is to close schools. We think that education is the priority for the country and that is simple social justice

He said: “But clearly what we are doing – the way we are trying to manage the Covid pandemic – is to have local measures in place and local test and trace to introduce restrictions where that’s necessary.

“But, as we have all said, the last thing we want to do is to close schools. We think that education is the priority for the country and that is simple social justice.”

The Prime Minister struck a conciliatory tone to education unions – who have raised concerns about the test and tracing system – praising the work that school staff had already done to make classrooms safe.

He said: “It’s very important that everybody works together to ensure that our schools are safe and they are – they are Covid secure – I have been very impressed by the work that the teachers have done, working with the unions, to make sure that all schools are safe to go back to in September.

“But, basically, the plan is there – get everybody back in September, that’s the right thing for everybody in this country.”

Mr Johnson said it was “not right” that children should spend any more time out of school, adding that it was more “damaging” for pupils who have fallen further behind amid school closures.

The Prime Minister said he understood there was “anxiety” about grades as pupils prepare to receive estimated results after exams were cancelled.

He said he was “very, very keen” that GCSE and A-level exams should go ahead as normal in the coming academic year.

Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), said heads supported the full reopening of schools in September and the pledge to make it a national priority.

But he added: “We are concerned about the lack of a national plan B if there is a second wave of coronavirus and there is a second national shutdown.

“The Government guidance requires schools to have in place their own contingency plans which are based on a return to remote education in the event of local closures.”

Mr Barton said: “We would like to see more thought given to blended learning as a back-up plan which could be a rota system of children in for one week and then learning at home for one week. This would be better than children returning solely to remote education.

“But we need some national modelling on how this might work informed by scientific advice so there is an off-the-shelf alternative that is ready to go.”

Greater Manchester 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, 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.”

Avis Gilmore, deputy general secretary of the National Education Union, said the union agrees with calls for a robust test, track and trace system to be in place to ensure the welfare of pupils and school staff.

She said: “Government could do much more to assure schools and local authorities that, should a second spike occur, either nationally or locally, there is a clear Plan B in place.

“This plan needs to spell out what action must be taken in a variety of situations, so that schools and colleges can make the preparations parents expect of them.”

But on Monday, a leading expert said children were “very minor players” in the transmission of coronavirus and opening schools would “add little” to the reproduction rate of infection.

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 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.

A Public Health England (PHE) analysis appears to show that Covid-19 outbreaks were “uncommon” in educational settings during the first month after the easing of national lockdown in England.

The study, which Mr Williamson and Prof Viner referenced, will be published in the coming weeks.

Care minister Helen Whately added it was the Government’s priority was to have children “fully” back at school by September.

Asked if schools should stay open in the event of a local lockdown, she told BBC Breakfast: “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.