A letter from an NHS nurse urging the government to keep schools closed because of the health risks to staff and the wider community has attracted more than 7,000 signatures, as teachers described trying to maintain social distancing in primary classrooms as “almost impossible”.

Iain Wilson, an NHS nurse with two children at school in Lewisham in south London, who has experience of working with Covid patients, wrote to ministers: “Do not make us the global guinea pigs. It is self-evidently unwise to force hundreds of people into small rooms in small buildings during a pandemic.

“Some teachers have already tragically died from the virus, and we do not want to risk any more,” wrote Wilson, a member of the Keep Our NHS Public campaign, in an open letter to the health secretary, Matt Hancock.

On Monday, as the summer term began with millions of children in lockdown, one headteacher described the challenge of trying to keep the small number of pupils currently in the emergency schools, which are open to vulnerable children and those of key workers, at a safe distance from each other.

“It’s almost impossible,” said Richard Sheriff, chief executive of the Red Kite Alliance, which runs nine primary schools and four secondary schools across Leeds and North Yorkshire. “We’ve got 56 children in one primary school this morning and the school is full because we’re using social distancing to keep them apart. Every time they move from a table, somebody comes and wipes it. Every time they use a badminton racquet, someone wipes the handle. It’s not easy.”

Pupils “returning” to school at home accessed more than a quarter of million lessons provided by the government’s new virtual academy, the Oak National Academy, which opened on Monday.

Created by more than 40 primary and secondary school teachers to keep children learning during the coronavirus lockdown, Oak aims to provide more than 180 lessons a week, with video tutorials and resources for teachers to support online learning already being provided by schools.

On its inaugural day, 140,000 students took part in an English lesson and almost 120,000 did maths, while the most popular single session was counting up to 10 for reception pupils, followed by reading comprehension for seven- and eight-year-olds. Poetry comprehension and Henry VIII were also popular.

On Sunday the education secretary, Gavin Williamson, moved to quell continuing speculation about schools reopening to all pupils, insisting that ministers would not contemplate it until the government’s five tests for beating the pandemic are met, but headteachers and local authorities are worried about the continuing uncertainty.

The tests are: protecting the NHS’s ability to cope; a fall in daily death rates; reliable data showing decreasing infection rates; confidence in testing and personal protective equipment (PPE) capacity; and confidence that changes to the government’s approach won’t risk a second peak of infections.

Many in the sector remain concerned, however, about not just when but how a return to school will be effected, and there are fears that the longer schools remain closed, the greater the loss of learning, particularly for more disadvantaged pupils who may struggle to engage with online lessons.

“Schools are working hard to deliver the best learning possible to pupils at home,” said Jules White, the headteacher at Tanbridge House school, Horsham, West Sussex. “The reality is, however, that self teaching is very hard even when there is strong family support.

“Whilst many issues need to be resolved for schools to open more fully, we must begin to think about further prioritising children who struggle most with learning and/or come from disadvantaged circumstances. When it’s safe they must get back into schools in larger numbers than we are seeing at present.”

Wilson’s letter warned: “Until we know that children will not learn that their teacher has died because of an infection caught in their class, we should remain sensible and wait.

“The economic harm of keeping schools closed is significant – but is known. This means the government can act and intervene to mitigate this harm. We do not know about the harms of reopening schools yet.”