And three-quarters say that there are not enough alternative-provision places for pupils with behavioural issues.
Almost 2,000 teachers, including 1,017 senior leaders, were asked the Department for Education-commissioned questions for the Teacher Voice survey, carried out by the National Foundation for Educational Research (NFER) organisation.
The results show that 84 per cent of school leaders say that there are not enough places in alternative provision for pupils with mental health needs.
Among secondary leaders, this proportion rises to 90 per cent and it is 77 per cent for primary leaders.
'More and more of a problem'
Geoff Barton, general secretary of the Association of School and College Leaders, said that this strength of opinion came as little surprise to him. "This will be getting to be more and more of a problem, as we see reductions in other services that might have been on hand," he said.
"For example, educational psychologists attached to the local authority, who perhaps now aren't available to schools."
In the Teacher Voice survey, 74 per cent of all school leaders report insufficient places in alternative provision for pupils with behavioural issues. The percentage was the same whether leaders were talking about pupils with or without special educational needs and disabilities.
A much smaller percentage – 25 per cent – say that there are not enough places for pupils with physical health needs.
Headteachers and leaders were also asked whether they felt there were enough quality places available for pupils in alternative provision.
Just over three-quarters – 78 per cent – of senior leaders say that there are insufficient quality places for pupils with mental health needs.
And two-thirds – 67 per cent – say that there are insufficient quality places for pupils with behavioural issues.
'Limited room for manouevre'
"Class sizes are going up in secondary," Mr Barton said. "Therefore, your room for manouevre as a headteacher is becoming more limited. What do you do with that child, even if you're committed to inclusion, if other children's learning is being disrupted?
"There's a desperate need, I'd say, for pupil-referral units and alternative provision, in the interests of these children."
The Department for Education has been contacted for comment.