A fifth of primary schools in England are full or over capacity and the problem is getting worse.
Government figures suggest that the number of children going to primary school will have risen by at least 700,000 by the end of the decade with the number of children beginning school this autumn 25% higher than previous years.
Education correspondent Gillian Hargreaves has been to Winchester in Hampshire, which has been hit by the rising number of children, to find out how the local council got into this situation and how it plans to resolve the problem.
Professor John Howson, educational analyst and visiting fellowship at Oxford University, told the Today programme's Sarah Montague that the sudden surge is due to a population of women who have postponed having children until older ages and also the surge in the number of migrants coming from Europe.
"We've known this boom has been coming and government have been tardy in responding," he said, adding that it is the "biggest problem facing schools in Britain".
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