I don’t know much about your healthcare system. I understand people who can pay can get private care, which may not be possible for your son. There is also the option to travel somewhere outside the country where the access to medicines is easier. (For example, adderall is available without a prescription in India. A flight from Heathrow to Mumbai costs about £355, according to the internet.)
Perhaps you can help your son by going to the GP with him and to help him push for a prescription without having to wait for an appointment with the Adult ADHD clinic. I found this article: http://www.dailymail.co.uk/health/article-1354640/Doctors-advice-How-best-GP-7-minutes.html If you get nowhere with the GP, maybe the approach of going in person will work at the Adult ADHD clinic.
No matter whether or not he can get help from the medical system, there are things he can do on his own. Maybe he needs your help to get started – or to persist.
All the best,