Sir Keir Starmer has called for schools to reopen as soon as possible and pleaded with unions, parents and government officials to work together.
The new leader of the Labour party also revealed his children have attended school throughout the coronavirus pandemic.
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Prime Minister Boris Johnson is currently facing a battle against more than 50 councils and teachers' unions to reopen primary schools in England on June 1.
British teaching unions have urged the Government to reconsider its plans to reopen schools for younger pupils in less than ten days.
In an interview with The Telegraph, Sir Keir said his 11-year-old son and nine-year-old daughter have continued to go to their local state schools in north London during the crisis as his wife Victoria is a key worker in the NHS.
However, Sir Keir acknowledged: "It's got to be safe.
"Our children have been in school throughout [the lockdown] and it's a reminder that this perception that schools are shut at the moment, and the question of whether we open them, is wrong.
"They're open at the moment, teachers, staff are on the frontline, every day.
"The question is, can we increase the numbers of children going back into school?
"I want that to happen as soon as it can."
The Labour leader added: "The task of the Prime Minister is to build consensus, to give people confidence.
"Most of the polling I've seen shows that parents are about 50/50.
"They're genuinely worried.
"Rather than accentuating the differences here, the Prime Minister should pull a task force together, and say 'Right, we are going to lead from the front'.
"If the Prime Minister said, 'I'll set up a task force of teaching unions, parents, local authorities and government, everybody else who needs to be around the table, to put your shoulder to the wheel, let's get on with this,' then I would certainly support that."
The Labour leader also called on a line to be drawn under the EU referendum result and Jeremy Corbyn's failed leadership as he told supporters 'the argument is over'.
He said: "We've left the EU, and therefore, the Leave/Remain argument is over and the only argument now is what sort of deal we have with the EU and what sort of deals we have with the rest of the world.
"It's very important for the Labour Party to be clear that whatever position we and others may have taken in the last three and a half, four years, that divide Leave and Remain are now over."
STUDY FINDS CHILDREN HALF AS LIKELY TO CATCH COVID-19
It comes after a major review found children were half as likely as adults to catch Covid-19, with lead scientists saying the results pointed "strongly towards a return to school".
Researchers at University College London (UCL) found that under-20s were 56 per cent less likely to contract coronavirus, concluding that "children are the safest group to be out in the community".
Today, Professor Russell Viner, senior author of the UCL report which says children have half the chance of catching coronavirus compared to adults, said schools should be allowed to reopen.
Speaking to BBC Radio 4's Today programme, the president of the Royal College of Paediatrics and Child Health said: "Children are the safest group to be out of lockdown, to be out in the wild.
"Covid-19 generally barely affects children and young people and actually we've shown that they are about half as susceptible.
"For children themselves, we need to balance the risk of not opening our schools for children's health and wellbeing, particularly their mental health, is high.
"I think there is no doubt in my mind for children themselves, the balances are clearly in favour of going back to school."
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Mr Johnson wants primaries in England in Reception, Year 1 and Year 6 to go back to class from a week on Monday, with others to follow in a "phased" restart.
But around 1,500 schools could defy plans to reopen.
And Justice Secretary Robert Buckland revealed he was not expecting everyone to be back by the June date.
Yesterday, coronavirus fatalities in the UK rose to 36,393 after 351 more deaths were recorded.
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