The findings raise doubts about whether thousands of children with special needs, ranging from behaviour disorders to physical disabilities, are being adequately provided for. And they call into question the Government's policies on inclusion.
The survey also reveals that thousands of teacher days are lost annually as a result of stress or injury caused by teaching children with special needs.
But despite their reservations, most teachers support inclusion where possible. Around a third of heads and teachers think children with special needs are most likely to achieve their potential in a mainstream school.
Almost half the heads and more than a third of classroom teachers believe that the education of other children is enhanced by special needs pupils.
However, almost two in three secondary heads and one in three primary heads say some of their pupils should be in a special school. This view is shared by classroom teachers, with three in 10 primary and more than half of secondary staff saying they teach at least one pupil who should be in a special school.
The poll shows huge support to save special schools, led by David Cameron, shadow education secretary in England and Tory leadership contender. Four out of five teachers and heads favour an end to further closures.
The survey of 511 classroom teachers and 206 heads in England and Wales, carried out by FDS International, suggests that as many as 15,000 primary and 10,000 secondary pupils who should be in special schools are in mainstream classrooms.
The Government has championed integrating special needs pupils. Legislation in 2001 strengthened their right in England to be educated at a mainstream school.
Since 1997, 93 special schools have closed in England, though the proportion of pupils attending them has remained constant. Baroness Warnock, who pioneered inclusion 27 years ago, earlier this year announced that the system was failing pupils. She said the TES poll showed there was an urgent need for the Government to review its inclusion policy.
"We need to look again at definitions of special needs and we need to target individual children much more closely," Lady Warnock commented.
Mark Vaughan of the Centre for Studies on Inclusive Education, said: "There needs to be disability awareness. Otherwise, you are dropping kids into a school where they are not welcome."
Almost 90 per cent of heads in the TES survey said their schools did not receive enough resources or support to ensure the success of inclusion.
Mick Brookes, general secretary of the National Association of Headteachers, said: "There is a conflict between ideology and resourcing.
It's expensive to teach these pupils in mainstream schools."