I think you need to come up with a plan with him in order to help him achieve his goal. Absolutely no reason he cannot use his savings to fund this IMO - it's HIS savings. I agree with the poster who said it may be easier if he waits till he's a little older. This would give him time to work on the factors that could hinder him.
I would consider he spends some of his money in some sort of help with his anxiety and lack of ability to socially interact with others. This is so important not just for communicating while learning to fly, but also in life generally. If he can learn some techniques to help with this, I would say that's money (his) very well spent. You'll have to seek advice/recommendations on who to use, but I would suggest try a local charity that helps locally with SEN as well as ask about locally for recommendations.
You need to discuss with him the need to converse with the instructor when learning to fly - or that'll be money down the drain and he'll never achieve it.
So he needs to prove that he can take instruction and ask for help while learning to fly, and to show initiative and act on it - he needs to be brave and try bus trips solo - you can initially send someone with him to sit away from him as back up for example, and to send him into shops solo to ask for and to buy things.
Until he can do this sort of thing solo, I really think it's be a waste of his money.
I would encourage him to retake his GCSE as in order to get a job post PPL (if he ever gets it) I'm quite sure he'll need it, and you say he is capable. I'd make English & Maths mandatory if he wants to then do his PPL.
I would suggest he learns to drive first, as it'll (more cheaply) give him an idea how to control the speed of an engine and how to steer. And will be so much more useful - if he can pass his test that is. Given his SEN needs, I'd perhaps go for an automatic lesson/series of lessons as there's a little less to think about.
For flying, I would see if you can find a trial lesson - has he ever flown in a small aircraft before? An example:
https://www.intotheblue.co.uk/experiences/flying-lessons-buckinghamshire/
He may find while he likes flying he doesn't actually want to control the plane/lacks the confidence to.
In which case you could steer him to some other plane related career.
If he does do his pilot's licence I always remember when one of my brothers did his - he kept disappearing to Guernsey for holidays. We all thought he had a secret girlfriend over there. Actually all it was was that the whole course was cheaper to do in Guernsey - he just didn't tell anyone!