Boris Johnson faces a revolt against plans to send children back to school in England on June 1.
Ministers failed to reassure teachers it was safe to reopen in a meeting with unions on Friday.
And as it was revealed the R rate of infection is rising, doctors echoed the teachers’ fears and the World Health Organisation said testing and contact-tracing had to be in place.
Liverpool is leading the revolt, telling parents kids will not return till June 15.
The plans are on the brink of collapse as teachers and city leaders prepare to defy the Prime Minister’s timetable.
Teaching unions warned that the Government evidence that reopening schools was safe is “flimsy at best”.
The British Medical Association said ministers should not consider reopening schools until coronavirus case numbers were “much lower”.
And the World Health Organisation urged the UK not to lift lockdown without contact-tracing in place.
They urged caution as it was revealed the R number had risen from between 0.5 and 0.7 on Sunday, when PM Johnson said restrictions could ease, to between 0.7 and 1.
The R value is a measure of how quickly the virus is spreading.
Parents in Liverpool today received a letter warning they should not expect schools to reopen on June 1.
Mayor Joe Anderson said he was “not going to take risks with children’s lives or with staff and teaching professionals’ lives.”
And Welsh First Minister Mark Drakeford said: “We won’t be bringing new cohorts of children back into schools on the 1st of June.”
After meeting union leaders, Education Secretary Gavin Williamson sought to reassure people that schools had the support they needed.
He said: “Getting children back to school is vital.”
But Dr Patrick Roach, NASUWT General Secretary, said: “Nothing in the meeting provided reassurance for the deeply worried and anxious school workforce.”
Chairman of the BMA Dr Chaand Nagpaul wrote to Kevin Courtney, the joint general secretary of the National Education Union, praising the union’s caution and saying the evidence for reopening schools was “conflicting”.
As schools across Europe began to reopen with distancing in place, secondary teacher Adam Boxer, 29, said any safety advice was impractical.
He said: “It’s all very well saying you need to keep your kids socially distanced where possible, but anyone who’s worked with six-year-olds knows that’s not really on the cards.”
At the No10 briefing, England’s deputy chief medical officer Dr Jenny Harries said it was unlikely small schools would have any infected pupils.
She said: “In a school with a hundred children, the likelihood of anyone having the disease is very small and diminishing with time.”
Health Secretary Matt Hancock refused to say if heads who decided the risk to teachers and staff was too great would face reprisals.
He said: “The risk to children is much, much lower than to anyone else.
"That means that we are able to propose going down this route of reopening schools.”
But WHO Special Envoy Dr David Nabarro told the BBC the capacity to “test, trace and isolate” was vital before restrictions are lifted.
The testing drive has been labelled a “shambles”, with just 1,500 contact tracers out of a promised 18,000 appointed by the start of the week.
Deaths rose by 384 yesterday to 33,998, with 236,711 people tested positive as of Friday morning.
No10 yesterday confirmed some parts of the country could be released from lockdown before others after modelling suggested London has just 24 new cases a day, compared with 4,320 in the North East and Yorkshire.
Steve Chalke, of the Oasis Trust, which has 35 primary schools, said they would admit pupils from June 1, insisting children as young as five were “very good” at social distancing.
Prof Saul Faust, infectious disease expert at Southampton University, said: “Society has to reopen.
Primary school leaders in England are planning to introduce one-way systems, smaller classes and half days to keep young children apart.
Springfield Primary School in Derby has closed for 14 days after two coronavirus cases were confirmed.
