It is "pure fantasy" to suggest that relaxing the social distancing rule will mean all pupils can return to school in September, heads have said.
And doubling the size of school "bubbles" to 30 in an effort to facilitate a full return is also not a "magic bullet", according to the Association of School and College Leaders (ASCL).
The comments follow today's announcement that the two-metre social distancing rule will be relaxed from 4 July, and the education secretary's suggestion last week that protective "bubbles" could be expanded from 15 pupils to the size of a whole class.
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Geoff Barton, ASCL general secretary, said: "There has been a lot of conjecture that relaxing the two-metre social distancing rule to one metre will allow all children to return to school in September.
"This is pure fantasy. It may be possible to accommodate more pupils in classrooms with a one-metre separation, but not all pupils. There just isn’t enough space in many classrooms to do this.
"It isn’t a magic bullet, and nor is the education secretary's suggestion on Friday of doubling the size of social bubbles to 30, in order to facilitate a full return to schools."
Mr Barton said it is hard to see how schools could keep bubbles apart "with pupils moving between different subject groups, and in playgrounds, corridors, sports fields, and transport to and from school".
The prime minister also today reiterated plans for all children to return to school in September.
Mary Bousted, joint general secretary of the NEU teaching union, said: "The NEU is of course in favour of all children being back in school, but even with a one-metre rule that will need more teachers and more spaces.
"It is not clear whether in less than three months the science will permit classes of 30. If social distancing of one metre remains in place, that will still be difficult for schools.
"Mathematics dictates that for this we need extra class spaces and extra teachers for the vast majority of schools. Government must support local authorities in making available public buildings, and encourage teachers who have left the profession, often due to excessive workload, to return."
She continued: "Employers and school leaders have been thinking through the implications of social distancing in their school for many months. One would be forgiven for thinking the government has not.
"For a safe return what we need to be hearing from the prime minister is not just hope, but pragmatism and a detailed, thought-through, strategic plan for schools based on the scientific evidence available.
"It is now more vital than ever that Boris Johnson and Gavin Williamson listen to the profession so that parents, teachers and pupils can be reassured that a return to school is as safe and as well planned out as possible for the whole school community and wider society."
Mr Barton added: "We need a proper strategy to bring children back into schools and colleges based in reality and on public health guidance."