More than 80,000 people have signed a petition arguing that no schools should reopen "before it is safe to do so".
The petition, launched by the NEU teaching union, has garnered the tens of thousands of signatures since it was started on Tuesday.
Mary Bousted, joint general secretary of the NEU, said: "I am pleased that so many have supported it and the number continues to grow.
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"As yet, there is no clarity as to how social distancing would – or even could – be implemented in schools, particularly for younger age groups.
"Even though the majority of children are considered low-risk, their teachers and families are not.
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"The fear is that asymptomatic children will put adult staff in danger, so it is essential that we see a programme of testing, PPE (personal protective equipment) and contact tracing throughout the education sector before schools are fully reopened."
The news comes as speculation over how schools can reopen has increased, with one prominent headteacher branding the idea that social distancing could be achieved in schools as a "lie".
The NEU called for an end to "disturbing" speculation over reopening schools earlier this week.
However, Labour leader Keir Starmer has called for schools to be reopened in the first stages of any end to the coronavirus lockdown, emphasising the impact that school closures will be having on disadvantaged children.
And writing today in Tes, Geoff Barton, general secretary of the Association of School and College Leaders, suggested that limited class sizes, staggered breaktimes and regular deep cleans of schools could be ways of reopening schools while preserving social distancing.
Noting that a vaccine for Covid-19 may be up to 18 months away, he said, "The stark fact is that a prolonged closure of schools will itself cause real harm to many children."