I know it has been a while since you posted this thread, but I just wanted to chime in with some information that I thought would be helpful to this topic.
Unfortunately we don’t know how many people in the UK have autism and Parkinson’s. But in some cases symptoms of autism crossover with symptoms of Parkinson’s such as bradykinesia (slowness of movement).
There have been some research studies looking into the link between autism and Parkinson’s and the results have shown that there may well be an increased frequency of Parkinsonism in older people with Autism. However the studies that have looked into this have been small so there needs to be further large scale research to replicate the results before definitive conclusions can be made.
I hope you find this helpful.