Parents of pupils with special educational needs and disabilities (SEND) "feel like schools don't want their children", say headteachers.
The demand for SEND support for children in early years education has doubled over the past five years.
The headteacher of St Philip's Marsh Nursery School in Bristol said the situation was "a bit brutal".
A council spokesperson said they were working with schools to "help mitigate national pressures".
Some pupils with SEND are held back in nursery for an extra year before starting primary school, local education bosses were told at a meeting of the schools forum at Bristol City Council.
Schools turn away prospective pupils for a variety of reasons, and sometimes being held back for a year can help a child's development, local headteachers said.
