The problem is most acute in rural areas and smaller towns, especially in Lincolnshire, Nottinghamshire and parts of the South West, said Mick Brookes.
He said some members of his National Association of Head Teachers complained they were at "breaking point".
There was a need for accurate national data on the scale of the problem, he plans to tell a House of Lords inquiry.
Schools might receive an extra £1,300 per year to support the needs of a foreign pupil, but the actual cost to the school could be £30,000, he said.
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