But a pioneering project in north London has made the dream a reality for two local schools. Teachers are reporting signs of dramatic improvements in the pupils involved.
Access to a professional psychologist is a walk down the corridor for pupils at John Kelly boys technology college in the London borough of Brent. Charles Welles, a counselling psychologist, offers counselling and social skills training to boys at risk of exclusion, as well as advice to teachers.
Christine Justic, assistant principal, believes it has changed the culture of the school.
She says: "There is a difference in the way we perceive issues. Perhaps the traditional focus on being very strict is less emphasised than support and guidance."
For the core group of boys at risk of exclusion who spend most time with Mr Welles, measuring the impact of the programme is more difficult. "We don't know what they would have done without him," says Ms Justic. But from Mr Welles's point of view, the contrast with out-of-school sessions is striking.
He says: "If the young person was going to an outside agency there would be a stigma, here it is just another part of the school."
Caroline Essenhigh, a child and adolescent psychotherapist, works at Camden's Chalcot school for pupils with emotional and behavioural difficulties, for one-and-a-half days a week. She provides therapy for pupils, support sessions for some parents, and advice for teachers.
Headteacher Elizabeth Hales says: "The boys who go to see her are boys who have resisted having treatment for their mental-health problems most of their lives. They have got to know her, they do not mistrust her, whereas a clinic is quite daunting.
"Quite often the boys come out of sessions quite distraught but here they are in a friendly environment, and they can get support from staff and friends."
A former head of an inner-city secondary, Ms Hales is in no doubt that on-site mental-health support should be extended to all schools.
"Looking back on it now, it is obvious that a large number of the pupils that we were overwhelmed with had unresolved mental-health issues that needed to be tackled. This is a service that is also needed in mainstream schools."