I do not have any personal experience of supporting someone with Autism, but in my involvement with LD I come across many people who do and many of the initiatives being developed for LD go under the Banner of LD or Autism. I would suggest looking at the National Autistic Website www.autism.org.uk this may give you some help or put you in touch with local groups that can help with activities.
I do not know which part of the country you are from but the situation of waiting times is similar where I live in the north west and we hear of cases taking well over 6 months for the first appointment and the diagnosis can extend over 12 to 18 months., one of the main reasons being the shortage of NHS trained clinicians I would add a word of caution in private diagnosis having heard of people paying for this, then the local authorities not recognising it. Make sure that anyone you use is approved by the local authority who will be responsible for commissioning support based on the diagnosis.
Check if there is a Autism Partnership Board in your area, this is a requirement but again can vary from area to area. Ours started last year and I attend just to improve my understanding as I an chair of trustees for the local Carers Service and we have family carers we support who are dealing with Autism and the isolation of their loved ones on a daily basis.