Well National Autistic Society Prospects Service may help. They have several schemes. One for people on disability/incapacity for voluntary work. One where you need a referral from the job centre which is a 20 week course including a voluntary placement then they help you find work at the end.
I just went for a more flexible one-to-one advice as I just want a part time job that is quiet. That is was free and they refund your travel expenses. However you will have to check in your area because some of these schemes are funded locally. They tend to be funded by different organizations/grants so they might have a variable level of bureaucracy/formality. I made it clear I didn't want any bureaucracy if I could help it. It was all more a case of it being suitable than training. I’m not sure how helpful their advice will be because you still look on the open market yourself. They can check organisations out on their policies and provisions and also help you write a cover letter.
I went to their London office in Islington for my first appointment. It was really just telling them want I wanted, gave CV, etc. She was very nice but she wasn’t especially clued up, but I have been assigned an employment consultant to work with me who might be better. Their own office was quite busy but the room I went to was booked at the regional office for NAS, which was next door and was quiet.
I would email prospects from the NAS website. I checked and Prospects is actually part of NAS not an employment agency associated with NAS.