Teachers' leaders have called for coronavirus testing for all school staff and rotas for those still working.
Dr Mary Bousted, joint general secretary for the NEU teaching union, also said better official advice for teachers on how they could stay safe during was needed.
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"We are concerned that government advice for schools is not currently strong enough," she said. "We have got to get on the front foot if we are to slow transmission and flatten the curve.
Call for coronavirus testing for teachers
“This means testing of all education staff, and that no one at heightened risk attends schools and colleges from today. No staff should attend who are vulnerable or would go home to family who are vulnerable. We also need to see coherent rotas for those who continue to go to their place of work."
Dr Bousted added that virus testing would be vital if schools were to remain open, as with so many parents employed as key workers, every school would need to be able to access tests.
"This is no time for half measures," she said.
She said government protocols on the distance pupils need to maintain between each other, and on hand-washing were needed to ensure safety, as while most children were "low risk" for contracting coronavirus they would still be carriers.
"So we must ensure that intensified cleanliness and minimised exposure rapidly become the norm in those schools which are having to remain open," she said.
The news follows reports this morning that a primary headteacher had died of coronavirus.
Wendy Jacobs, the headteacher of Roose Community Primary School in Barrow in Furness, Cumbria, died after being admitted to intensive care with coronavirus symptoms.
Headteachers have expressed frustration over the lack of help they feel they have received from the government.
Vic Goddard, the co-principal of Passmores Academy, in Harlow, Essex, who led a grassroots campaign for ministers to provide supermarket vouchers for pupils eligible for free school meals during school closures, tweeted yesterday that he had been asking for help from the government all day.
Been asking for help from govt all day. I am angry, frustrated and scared. I’m being asked to make life and death decisions for my own and other’s families. I have received great support from @halfon4harlowMP but what will it take for govt to be leaders? Scared to answer this— Vic Goddard (@vicgoddard) March 22, 2020
Dr Bousted said the NEU were liaising with the Department for Education to ensure schools had "maximum protection" from the government.
The DfE has been contacted for comment.