It said a particular problem was the huge variation in what was being charged by non-NHS providers.

Unlike for routine operations, like hip and knee replacements, where there is a set tariff for different treatments regardless of whether the NHS or private sector carry them out, for autism and ADHD there are only guide prices that do not have to be kept to.

Local health bosses have also reported a rapid increase in providers. One board reported working with 48 providers – four times more than in two years previously.

This expansion was causing problems with the ability of boards to check the quality and safety of the care and support being provided.

Providers who carry out assessments only do not have to be registered with the Care Quality Commission, the regulatory body for health and care.

Rebecca Gray of the NHS Alliance said managers were “caught between a rock and a hard place”.

“They understand the anguish and frustration caused by long delays in the system as people wait for assessments, treatment and support.

“But in working to meeting demand they face soaring costs that are running out of control.”

She said the situation was a “bad deal for patients and taxpayers” and there was a risk the whole system would fall into “chaos”.

But a spokeswoman for the Independent Healthcare Providers Network said private providers were helping the NHS meet the growing demand by bringing “significant capacity and innovation”.

However, she agreed there needed to be better co-ordination, including a national tariff to ensure consistent prices were paid by the NHS.

Mel Merritt, of the National Autistic Society, said it was clear the system was in crisis.

“Spending is rising on short-term solutions due to years of a lack of long-term investment in improving services.”

And she added despite the sums being spent people were still facing “unacceptable” delays.