@StefanieThanks so much for sharing your experience, and I'm sorry to hear your son is now facing a long waiting list. Have you investigated a referral from your GP using 'right to choose'? I'm not entirely sure how the process works, but this info from ADHD Aware might help https://adhdaware.org.uk/what-is-adhd/getting-nhs-diagnosis/right-to-choose/
You make a really important point about the role of schools, it seems like they would be well placed to help students in your son's position. However, I know schools are also facing huge funding issues and many schools are having to reduce interventions like bringing educational psychologist services. I don't know how much the Government's SEND Improvement Plan will make a difference to accessing ADHD assessment.