Fully reopening schools without substantial improvements in the performance of the test-and-trace system could risk a new surge in cases of Covid-19, according to calculations by the government’s scientific advisers. A report presented to the Scientific Advisory Group for Emergencies (Sage) on 20 May, at a time when the government was weighing up the impact of school reopening in England, indicated little leeway for increasing school attendance and relaxing other physical distancing measures without a test-and-trace system that reaches 80% of contacts within 48 hours. “Highly effective contact tracing would give us much more room to manoeuvre, but even in that scenario, if all schools are reopened, some kind of social distancing would still be required,” the scientists suggest. The scientists caution that the modelling is not designed to give precise predictions, and circumstances have changed since the calculations were made. But as a general indication of the importance of test and trace, the model suggested that with highly effective contact tracing it would be possible to fully reopen schools and resume social contacts at 60% of normal levels without the R rate returning above the critical value of 1. With only ineffective contact tracing – 20% of contacts reached - active work and leisure contacts would need to stay at 20% of normal levels for schools to fully reopen and avoid a rise in the number of cases. The calculations do not suggest that school reopenings are the most critical measure for increasing infections, but they illustrate the importance the scientists place on test and trace. The recommendation that an effective system should reach 80% of contacts within 48 hours has been reiterated at various meetings in recent months. This is significantly above current performance. Government figures released on Thursday show that, of those who test positive, 70.3% were reached, with about three-quarters providing details for close contacts and the rest saying they had no recent close contacts. Of the contacts provided, 81.7% were reached. It is unclear what proportion are tracked within 48 hours or how many follow advice to self-isolate. The most optimistic estimate for current performance is that 57% of contacts are being traced rapidly and isolating, but the true proportion is likely to be lower. The government has been at loggerheads for weeks with teaching unions, who claim plans to reopen schools while maintaining physical distancing are fanciful. Concerns have been raised that children, particularly those from disadvantaged backgrounds, will fall behind in their education if schools do not reopen, but unions have maintained that doing so must be safe and practical. The phased opening of schools in England began at the beginning of June, but the government shelved plans to get every primary school child back in class for at least a month before the summer holiday, in the face of the opposition from unionsand some scientists. Boris Johnson announced on Tuesday that there would be full attendance at schools in September, as he detailed how the lockdown would be eased, but unions said that was still unrealistic. Geoff Barton, the general secretary of the Association of School and College Leaders (ASCL), said that even with the physical distancing rule reduced to 1 metre, it was “pure fantasy” to imagine schools would have the space to take back all pupils. The National Education Union said more teachers would be needed. Christina Pagel, a scientist at University College London and a member of Sage, said the decision to relax restrictions was a concern, given the proportion of people currently being reached by test and trace. “America’s seen a massive surge and I’m worried we’re going to be in a situation here where we don’t spot these increases until it’s too late,” she said. Changes such as pub and restaurant openings planned for 4 July in England were a greater source of concern than the prospect of schools fully reopening in September, she said. When Johnson announced the September plan, he said: “Children who can already go to school should do so because it is safe.” Only a minority of children eligible to return to school in England, however, have done so.