The British Medical Association has thrown its weight behind teaching unions opposing the government’s push to reopen schools in England, as the debate over millions of pupils returning to classrooms grew increasingly acrimonious.

No 10 reinforced its drive to reopen primary schools for those in reception, year 1 and year 6 in two weeks’ time, warning that prolonged closures risked damaging children’s education.

But the BMA – the UK’s largest doctors’ union – said in a letter to the National Education Union on Friday that the number of coronavirus infections remained too high to allow them to run safely. Teaching unions had been “absolutely right” to urge caution and prioritise testing before reopening schools on 1 June.

“We cannot risk a second spike or take actions which would increase the spread of this virus, particularly as we see sustained rates of infection across the UK,” the BMA council’s chair, Chaand Nagpaul, said in the letter to his NEU counterpart, Kevin Courtney.

The BMA said there was conflicting evidence from scientific studies on the effect of reopening schools, citing the “relatively small amount of research available and the uncharted territory we find ourselves in”. Nagpaul concluded: “Until we have got case numbers much lower, we should not consider reopening schools.”

Meanwhile, Liverpool became the first local authority to rule out reopening its schools until at least 15 June, in a significant blow to the government.

Liverpool’s move may encourage other local authorities to follow suit. With most state primary schools still maintained by councils, that could mean many schools missing the government’s 1 June target. Liverpool city council maintains 109 primary schools.

Some academy chains have said they will go ahead on 1 June, however. Steve Chalke, founder of the Oasis multi-academy trust, which runs more than 30 primary schools, called the opposition to reopening “rather middle-class” and accused teachers’ unions of failing to recognise the harm being done to disadvantaged children.

In the face of scepticism from teachers and school leaders, the government has increasingly raised the stakes in recent days. The education secretary for England, Gavin Williamson, wrote in the Daily Mail that teachers should be ready to “do their duty” and cooperate with the government’s efforts.

Boris Johnson’s official spokesman said: “Safety comes first, but we must also be aware of the potential damage to a child’s education from not getting them back in the classroom.”

Part of the government’s effort to win over the sector saw it hold a large virtual meeting on Friday between education leaders from colleges, schools and nurseries and top medical and scientific advisers, including Chris Whitty, the chief medical officer for England, and Patrick Vallance, the UK government’s chief scientific adviser.

But union leaders said they were “left with more questions than answers” after the meeting, which some participants said was at times confusing and chaotic, with around 50 people and organisations taking part. Some complained that their questions were not answered.

Patrick Roach, general secretary of the NASUWT, said the evidence presented to the meeting was “flimsy at best” but that there was room for further discussion.

“This was never in our minds a make-or-break meeting, that was never its purpose. It’s for the government to demonstrate that the scientific advice is there, and then it’s for schools and government to demonstrate that schools will be safe for reopening, from whatever date,” Roach said.

“It’s vitally important that the government and employers are behaving reasonably. It’s disappointing that many of the questions that we put to the scientific advisers this afternoon haven’t yet been answered. We hope that they will be answered – our members are hoping they will be answered.

“The government has got to win the confidence of the profession, and it’s got to win public confidence as well, if parents are going to entrust their children into schools where there is a risk of greater transmission of the virus.”

The NEU’s Courtney welcomed Vallance’s pledge to publish the papers presented to the Sage group of government advisers relating to education. But he also said the scientific advice presented to the meeting appeared mixed, and he was surprised to learn of instances in Australia where children had carried coronavirus cases into their households as “index cases”.

“The things that they told us didn’t give me confidence that we should be going ahead without the social distancing and measures that schools in other countries have. It’s really not clear what the government’s test is to reopen schools,” Courtney said.

The governments in Wales and Scotland remain unmoved by Westminster’s decision to reopen schools. Nicola Sturgeon, Scotland’s first minister, said: “There will be no cavalier approach to any aspect of this on the part of the Scottish government.

“It is not going to be the case that schools are back to normal in any way, shape or form this side of the summer holidays. We are of course discussing if it is possible for any pupils to be back in that timescale. But if it is, it is likely to be on a very limited basis.”

Kirsty Williams, the Welsh education minister, also said no date had been set for schools there to reopen. But she announced the publication of a working document to stimulate discussion over how to reopen.

“Setting a date before we have more evidence, more confidence and more control over the virus would be the wrong thing to do,” Williams said.

The health secretary, Matt Hancock, said at Friday’s Downing Street press conference: “I wouldn’t support a proposal to start to reopen schools unless it was safe to do so, and it is safe to do so.”

He added: “In the same way that it’s terrible news that this virus impacts on the elderly so much, the good news is that it seems to spare children in almost every case. And so the the risk to children is much, much lower than to any other age group – certainly if you don’t have underlying health conditions.”

The deputy chief medical officer for England, Jenny Harries, said the falling number of cases across the community would reduce the risks further in coming weeks. “There’s a lot of anxiety I think around this, but people need to think through, in an average infant school of maybe 100 children, the likelihood of anybody having this disease is very small, and diminishing with time, so we just need to keep that in perspective.”

Williamson said: “Getting children back to school is vital for their educational development and many schools are already taking steps to welcome back their pupils. I am grateful for their support.”