Boris Johnson is under pressure to publish a back-up plan designed to keep schools open if there is another Covid-19 spike.

Unions have warned the Government needs an alternative if cases start rising from September.

Mr Johnson has said getting all children in England back to school full-time next month is the “right thing for everybody”.

Even schools in swathes of the North West that have undergone further restrictions due to sharp rises in coronavirus cases will be expected to open.

One union said ministers should consider a “week-on, week-off” rota system for pupils if there are further lockdowns.

But the Prime Minister said he hoped schools would not be forced to close by local leaders.

He said on a school visit in East London: “Clearly what we are doing – the way we are trying to manage the pandemic – is to have local measures in place and local test and trace to introduce restrictions where that’s necessary.

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The government wants all children back to school by September

“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 PM is facing calls to dramatically overhaul the national test and trace system to safely reopen schools – without imposing further restrictions on businesses or social lives.

But he has been warned by his scientific advisers that “trade-offs” may be necessary to keep transmission rates down.

They have claimed the nation may have reached the limit of what can be reopened safely.

No10 confirmed yesterday that pubs and restaurants might have to shut to keep schools open in a local lockdown.

Mr Johnson’s official spokesman said: “It’s correct to say schools would be the absolute last sector to close in any local lockdown.

“Other venues would be expected to be closed first in the event that strict lockdown measures had to be applied.”

Britain's Prime Minister Boris Johnson gestures as he visits St Joseph's Catholic School in London

Geoff Barton, general secretary of the Association of School and College Leaders, 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 added: “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.”

Avis Gilmore, of the National Education Union, added: “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.

Thai children wear face masks as they play in screened-off play areas at a school in Bangkok

“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.”

The PM struck a more conciliatory tone to education unions after months of attacking them - 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.”

Leading expert Professor Russell Viner said the week on-week off proposal appeared to make “very little difference” to the overall risk to both pupils and teachers.

The president of the Royal College of Paediatrics and Child Health said that children are “very minor players” in the transmission of coronavirus and opening schools would “add little” to the reproduction rate of infection.

Prof Viner, also a member of the Government’s Sage scientific advisory group, said that reopening schools is “one of the least risky things we can do”.

Britain's Prime Minister Boris Johnson gestures as he visits St Joseph's Catholic School in London

Schools in Scotland go back today [TUES] while Welsh first minister Mark Drakeford has said that in Wales, some schools could be forced to close in the event of a local outbreak.

“Every local flare-up is different; in some places not reopening schools would be part of a plan, in other sorts of outbreaks that may not be necessary. It’s down to the local circumstances, down to the team on the ground. and they will then advise Welsh ministers,” he said.

Greater Manchester mayor Andy Burnham said that ‘test and trace’ had to be better to give parents the confidence to send their children back to school.

He called on the Government to give more resources to local councils - a handful of which are setting up their own schemes - to trace people the national call centres were unable to reach.

Mr Johnson also said he understood the “anxiety” over exam grades as pupils prepare to receive estimated results this week for A-levels cancelled during lockdown.

Scotland’s First Minister Nicola Sturgeon has apologised for the handling of exam results after those estimated by teachers were downgraded more in poorer areas than affluent ones.