Ministers’ plans to reopen schools as early as 1 June are in serious doubt after unions representing teachers and school staff insisted that they would not consider a return without a stringent coronavirus “test and trace” regime. In an unusual joint statement, which one senior union official said indicated that an early return to a normal school timetable was “off the menu”, the Trades Union Congress said that there should be “no increase in pupil numbers until full rollout of a national test and trace scheme”, and called for the establishment of a Covid-19 taskforce with government, unions and others to agree on the safe reopening of schools. But with a national strategy for a scheme that would help identify who needs to be in quarantine yet to be deployed – and a contact-tracing phone app still undergoing a limited trial on the Isle of Wight – the unions’ tests are unlikely to be satisfied by the 1 June date floated by officials last week. That could mean children in England and Wales returning to schools for just a few weeks between now and the new school year in September, and pupils in Scotland – who break up earlier – increasingly unlikely to return before the summer holidays at all. The Scottish and Welsh governments have already announced that their schools will not reopen on 1 June. The news comes amid growing signs that Boris Johnson will set out a cautious “roadmap” for the next phase of the crisis on Sunday after the government faced severe criticism over its mixed messages about what the public should expect. The statement, submitted to the education secretary, Gavin Williamson, is backed by the main teaching unions, as well as Unite, GMB and Unison, which represent key school staff such as cleaners, administrators and caterers. Any return without their agreement is highly unlikely. “The wider reopening of our schools will depend greatly on ensuring that families and carers are fully confident that allowing their children to return to school is safe. We do not believe that sufficient levels of confidence exist at this time,” it said. Johnson told last weekend’s Sun on Sunday: “One of the things we want to do as fast as we can is get primary schools back. It’s not going to be easy, but that’s where we want to go. It’s about working out a way to do it.” Whitehall sources suggested at the time he had in mind a phased return from the beginning of June, after the summer half-term break. But the Guardian understands that conversations with headteachers and trade unions in recent days have underlined the practical challenges of the move – and the potential resistance from parents anxious about their children’s safety. A government source insisted on Friday: “We never set a date.” Ahead of Johnson’s address to the nation, the environment secretary, George Eustice, on Friday played down suggestions of any major changes to the lockdown regime, stressing that the government would proceed “with the utmost caution”. At the press briefing, Eustice also stressed the importance of abiding by the existing measures over the bank holiday weekend, despite the fact that the government is poised to allow unlimited exercise, sunbathing and picnics from Monday. But he welcomed moves by some businesses to reopen where existing restrictions already allow – including McDonald’s. “Our view is that McDonald’s drive-through is made for the social distancing system that we are in,” he said. The Welsh government stole a march on Johnson on Friday by announcing a three-week extension to its coronavirus lockdown and making modest adjustments, including allowing outdoor exercise more than once a day and plans to reopen libraries. The first minister, Mark Drakeford, insisted that the lockdown needed to stay, but said “very cautious” changes would come into force. He anticipated that “broadly” similar changes would be announced by the prime minister. He said that from Monday, people would be allowed to exercise more than once a day, provided that they do not travel “a significant distance” from their home. Garden centres will be allowed to reopen if they can ensure that the 2-metre physical distancing rule is enforced. And councils will begin work on plans to safely reopen libraries and municipal recycling centres. The announcement came as Scotland’s first minister, Nicola Sturgeon, said she believed “all four nations now accept there may be differences in pace of how we do these things because the level of the virus is at different stages”, although she expected divergence from England’s upcoming new guidance to be minor. The TUC’s tests include “clear scientific published evidence” that reopening schools will not increase the transmission of Covid-19; agreement between government, unions and employers over minimum safety standards for social distancing and hygiene; and a ”secure supply” of PPE for school staff. But the key demand is that opening up schools cannot begin until there is a “full rollout” of the government’s test, trace and isolate policy, with targets for testing being consistently met and the numbers of new cases of Covid-19 falling. Williamson has maintained that his top priority is the safety of children, and said that the question of when and how to reopen schools is the government’s most difficult decision. The teaching unions and the Department for Education have been consulting closely in recent days, with ministers and advisers contacting individual headteachers and academy leaders to canvass their views. Following the discussions, the DfE believes the TUC’s tests do not differ significantly from those set out by the government to end the lockdown. Michael Veale, a lecturer in digital rights and regulation at University College London who has been involved in the development of coronavirus tracing apps in countries including Switzerland and Germany, said it was possible that the first NHS tracing app could be ready by 1 June. But he warned that an app alone would be unlikely to be sufficient to curb a Covid-19 outbreak affecting schools. “The question is, would an app help schools?” he said. “Primary schools don’t contain humans with smartphones in the same way as the rest of the world. Certainly, unions should be alert to health risks for the workers they represent, but I don’t think unions should rely on an app to protect their workers. They should make demands that relate to broader tracking and tracing capabilities.” Veale said that an underlying problem in the UK was its failure to conduct enough tests to make tracing work effectively, even with a functioning app available. The first version of the NHS app requires users to self-report symptoms. “We must be careful not to make strong claims about the effectiveness of an app before we have even deployed one,” he said. The health secretary, Matt Hancock, has claimed that a nationwide contact-tracing scheme, involving 18,000 contact tracers, will be in place by mid-May. But he has conceded that it is a “huge national undertaking of unprecedented scale and complexity”. The NASUWT teaching union has already called for schools to remain closed until the end of the summer holidays, while the National Association of Head Teachers said it is “clear that parents are very nervous about sending their children back to school”. A DfE spokesperson said: “Schools will remain closed, except for children of critical workers and vulnerable children, until the scientific advice indicates it is the right time to re-open and the five tests set out by government to beat this virus have been met. “We are also working closely with the sector as we consider how to reopen schools, nurseries and colleges and will ensure everyone has sufficient notice to plan and prepare.”