The Government's own advice from SAGE experts cast doubt over whether to reopen schools next month, saying there was still "some risk".
Evidence on how likely children are to transmit Covid-19 remains "inconclusive", according to scientific advice used to inform proposals to reopen schools from June 1.
Wider issues - including whether families have black, Asian and minority ethnic (BAME) members - must be taken into account when assessing the impact of relaxing school closures on transmission, according to papers from the Scientific Advisory Group for Emergencies.
Teachers do not appear to be at a greater risk of catching Covid-19 than other professions - but there is still some risk if schools reopen, scientific advisers have said.
The SAGE papers suggest that younger teachers' attendance in schools could be prioritised in order to decrease the likelihood of infection for school staff in more vulnerable groups.
Publication of the advice comes after education unions and council leaders called for the evidence underpinning the proposal to reopen schools in England to be released.
The SAGE advice was from March but has just been published today.
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Scientists advising the British government have said children have milder Covid-19 symptoms than adults and the balance of evidence suggests that children may have lower susceptibility and infectivity than adults.
The group of scientists concluded "that there was some evidence that children had milder symptoms than adults but that evidence on susceptibility and transmission was as yet unclear and recommended consideration of additional data gathering."
"Evidence remains inconclusive on both the susceptibility and infectivity of children, but the balance of evidence suggests that both may be lower than in adults," the scientists said in papers submitted to the British government up to end of April.
"Serological studies are starting to be available on child infection history, with some suggestinglow rates of infection.
The scientists said a robust testing and tracing system would be needed for schools to fully reopen.
No10 has been under pressure for weeks to make the advice public amid a row with teaching unions over their coronavirus safety concerns, a rebellion from councils and doubts that schools would be ready to reopen 10 days from now.
It comes after scientists from a committee called Independent Sage warned it would be unsafe to reopen schools to more Reception, Year 1 and Year 6 pupils on June 1.
The group, led by former chief scientific adviser Sir David King, claims Boris Johnson's target is too soon and the risk to children would be halved if ministers delayed the planned reopening by two weeks.
Teaching unions have express concerns about safety and pressured the Government to delay the reopening of schools. They have told their members they should not go to work if they feel unsafe.
Several councils have said they will not reopen their schools on June 1 or they will leave it to individual schools to decide based on a risk assessment.
It means hundreds of schools could remain closed if Downing Street sticks to its June 1 target.
A BBC Breakfast survey found that scores of councils say they cannot guarantee primaries will reopen on June 1.
Only 20 of 99 English councils which responded to the survey were advising schools to open more widely that day.
Two-thirds (68) warned that their schools may not reopen to Reception, Year 1 and Year 6 on June 1 as planned, the survey found.
Fifteen local authorities, most in the North West of England, said they were refusing to advise schools to reopen, 53 were allowing schools to make an individual decision, and 11 were still considering the issue.
TUC, an umbrella group which represents a majority of trade unions in England and Wales, said a lack of planning risks a chaotic reopening.
Frances O’Grady, the organisation's secretary general, has urged Education Secretary Gavin Williamson to set up a taskforce, which would include union reps, to avoid a “last-minute” approach.
She said the Government risked repeating “the chaos and confusion the Prime Minister’s back-to-work announcement caused”.
She told the Guardian: “Getting kids back into the classroom must be done in a safe and planned way. As it has done in other sectors, the government urgently needs to a set up a Covid-19 education taskforce with unions and other key stakeholders. We have been pressing Gavin Williamson for this."
She added: “This will help give confidence to staff and parents, many of whom currently feel in limbo.”

Experts on Sage have suggested the decision to reopen schools to younger children is rotted in concern for their welfare rather than scientific evidence, the Telegraph reported.
Modelling suggests there is little evidence to show that different year groups are at higher risk from Covid-19, a source on Sage's subcommittee on schools told the newspaper.
The source added: "Any decisions regarding particular year groups should be made on welfare reasons and education reasons, because there isn't the modelling to suggest different age groups are more at risk than others."
Sources said the reopening plan was "absolutely" conditional on a contact tracing system being operational.
Boris Johnson has insisted a tracing system will be ready for June 1. Children currently face being sent back to school before a tracing app is in place across England, however.
A Sage source told the Telegraph that much of the committee's work for lifting lockdown measures was based on a tracing system being operational.
The source said of the plan for schools: "Any decisions regarding particular year groups will be made on welfare reasons and education reasons."
Schools, colleges and nurseries across the UK closed more than eight weeks ago due to the coronavirus outbreak, remaining open only for vulnerable pupils and the children of key workers.

Mr Johnson unveiled proposals to allow more children in Reception, Year 1 and Year 6 to return to school in England from as early as June 1 as part of his strategy for easing lockdown restrictions.
It is his hope that primary schools will be open for children of all ages by the end of June, giving them a month of lessons before the summer break.
But the devolved administrations in Scotland, Northern Ireland and Wales have adopted different approaches to sending children back to the classroom.
A spokesman for the Department for Education said: “We want children back in schools as soon as possible because being with their teachers and friends is so important for their education and their wellbeing.
“Plans for a cautious, phased return of some year groups from 1 June, at the earliest, are based on the best scientific and medical advice.
"The welfare of children and staff has been at the heart of all decision making.
“We have engaged closely with a range of relevant organisations, including the unions, throughout the past eight weeks, including organising for them to hear directly from the government’s scientific advisers last Friday, and will continue to do so.
"We have also published detailed guidance on the protective measures schools should take to reduce the risk of transmission.”
Mr Johnson insisted a Covid-19 tracing system will be in place by June 1 when he was challenged by Labour leader Sir Keir Starmer during Prime Minister's Questions on Wednesday.
An NHS contact tracing app currently being trialled on the Isle of Wight has been beset by problems, delaying its launch in England.
It was meant to be launched across England in mid-May and it will not be ready for June 1, Downing Street has confirmed.
What are the plans for different nations?
England
The Government expects pre-school children to be able to return to early years settings, and for Reception, Year 1 and Year 6 pupils to be back in school, from the start of next month.
Young children could start returning to nurseries and primary schools in England from June 1, with the Government aiming for all primary school pupils to go back for a month before the summer holidays.
The Government has also said secondary schools and colleges should aim to offer some "face-to-face contact" with Year 10 and 12 students who have key exams next year during the summer term.
A final decision on whether to go ahead with reopening schools is expected to be taken by the Government on or before May 28 after the most up-to-date scientific evidence has been reviewed.
Scotland
Teachers will return to school during June to prepare for the attendance of pupils, while there will be support where available for pupils moving into primary 1 or moving from primary to secondary school.
Education Secretary John Swinney said parts of the school estate could be expanded to allow social distancing to be observed, and community and leisure centres, conference halls and libraries could be used to allow pupils to spend more time with teachers.
Schools will reopen towards the end of the summer holidays in Scotland, but children will return to a "blended model of part-time in-school and part-time at-home learning" to allow for social distancing.
Northern Ireland
All children are intended to restart classes on a phased basis, involving a mixture of physical attendance and remote learning, in September if enough progress is made in curbing coronavirus.
But the education minister has said schools in Northern Ireland could reopen to pupils preparing for exams in the third week of August.
Those studying for major public tests and transfer from primary to post-primary schools would be among the first to return to classes under an envisaged phased reopening, Peter Weir said.
Exams for entrance to post-primary schools are due to be held two weeks later this autumn to allow more time for primary teachers to catch up on lost lesson time since the school closures.
Wales
The Welsh Government has not given any dates for when the country can expect schools to reopen.
Wales' plan to exit the lockdown sets out that restrictions will be eased through three stages - red, amber and green - and each of the stages will see a "cautious" lifting of measures.
If the virus remains under control, the amber zone would follow and include allowing priority groups of pupils to return to school. Further control of the virus would move the country into the green zone, allowing all education to resume.
Education minister Kirsty Williams said she would refuse to set an "arbitrary date" for a return to schools, saying the Government first needed to see more evidence about the disease.