I never had an indoor cat, especially in the UK. I am familiar with their behavior as I had plenty of outdoor cats.
My son is slightly autistic, I have no idea if it is advisable to have my boy and pet/cat under the same roof.
Both my daughter (16) and son (13) are high-level autistic (would have been called aspie by the old yardstick). We've had cats their entire lives.
Currently we have two cats, a big black labrador, and two guinea pigs. In the past we've also had goldfish and hermit crabs. They've been very good with the pets overall. The cats certainly make a lot more sense to them then people as all cats have asperger syndrome.
Agree with the good suggestions from other answerers: take your son to an animal shelter or a friend-with-cats place and acclimatise him a bit first. Also consider getting a three or four year old cat, rather than a kitten. A good natured older cat may work better than a zooming little fur ball that hasn't yet figured out that it should retract its claws while running over carpet.
You may have heard the expression "if you've seen one child with autism, you've seen ONE child with autism". "autism" covers such a wide range of behaviors and experiences that it's really hard to make general predictions. Furthermore, age is a big factor here with all children (and cats, for that matter), autistic or not. That said, Dalton's reasoning makes a lot of sense, inasmuch as generalizations can be made.
My 9-year-old, who is also "slightly autistic", gets along great with other people's cats (we don't have any of our own yet), but it took him some time to learn how to approach them. Early on, he was too eager to approach the cats, they ran away, and he had a tough time dealing with his frustration.
Instead of getting a cat right away, consider taking him to an animal shelter, to see how he's interacting with cats and to teach him how to interact with them.
I can't remember the name of it, but I was watching a program on Nat Geo or Discovery the other day and there was a semi-autistic child who didn't interact with the adults much until they got a cat and it really brought him out of his shell. I think they were saying that several cat behaviors appeal to autistic people. For instance, cat's don't prefer to make eye contact. They also aren't very noisy (some cats are very noisy), and they're fairly passive aggressive about attention. I'm not saying that it will absolutely work for you, because it depends on the person as well as the cat. My aunt has a kitten who's a little hellion on speed, but plenty of cats are calm. I think it's really worth looking into.
Also, just remembered a grown man with autism on the show 'Must Love Cats'. He had the same deal going on. Ended up building walkways all through their house for his cats. You can probably find that on youtube.
Like some people say, take him to a shelter and see how he reacts with animals...In addition to that, I will give an advice: if you decide to get a cat, choose a older one. Why? Older cats (more than 1 yo) have their character defined, if they say: "he/she is very kind", it's 99.9% true. A kitty...yeah, they're stinking cute, but also a time bomb: you don't know how they will be in the future! Cats are like people, aaall different. Good luck :)
Perhaps you could find a friend with a friendly cat or two and see how he gets on with them?
I have no experience of this, but I would note that both cats and autistic children like regular routines, which would suggest that they would complement each other.
My kids are not autistic, so I don't have any experience to you here. I do, however, have quite a but experience with cats, and cats & my kids.
Our cats have always been indoor cats, and in my mind they behave very similar to outdoors cats, or any cats not 'feral'. Even the barn kitty at the barn I board is very similar, she wants to be petted and purrs and runs away when scared.
My boys are 2 and 5, and quite energetic. They don't take the greatest care with their toys, they like to wrestle, and they sometimes struggle to use words and not their arms when disagreeing. They are sometimes rough with the cats. The older cat just avoids them. We had him long before we had kids, and he has no patience for them and their noise. The kitten, which we got after the kids, are more patient, and will accept a lot more noise and energy.
We do need to constantly remind the kids to be gentle with the cats. They do want to pet them and hug and play with them, but sometimes they forget they can't pull their tails. They forget that if the cat doesn't want to play, he walks away. They forget that dangling the toys in front of the cat is better than on top of the cat... it is a lot easier for the 5 year old than the 2 year old to remember this.
It is all part of learning how to behave with animals. I have seen some kids who are naturally more gentle. I think you probably know if you kid will be gentle (autism or not), and if they will be able to learn to be.
As for a cat, a cat will walk away if not happy. A cat will also lash out if cornered. They take care of themselves, and I think that is good - but you have to be prepared that a scratch may happen.
I do recommend a younger cat or kitten, so it can become used to your kid right away. I personally think an older cat only works with older kids or adults, but I know opinions on this wary.