I want to get a dog but I have to work, how does everyone on broadway market do it ?

This sounds like a really difficult situation. Dogs are allowed off-lead loads of places and will often come over and say hi to people. 9 times out of 10 it's well received, and the reverse situation happens tonnes too (humans going over to pet dogs, uninvited). So dog owners are not conditioned to think it's a bad thing. Obviously when your son reacts like that people should recall their dogs. But I'm not surprised that many don't, as dog owners like any other group of people contain plenty of wrong-uns, weirdoes, thoughtless or just distracted people.

I think the legality of the situation is a bit of a red herring. You are not going to find the police taking an interest, and even if they did they're not going to be around to prevent it the next time.

I think grudgingly you are going to have to accept that this is a thing that will happen sometimes, and work on what you can do to make it less shit when it happens. I'm not in any way saying it's your or your son's fault of course - but just that you are not going to be able to change other people's (or dogs') behaviour.

What would you do if your son has a similar reaction to say cats or pigeons or something else coming up to him? Is there any way you could familiarize him with a friend's or family member's dog (small, cute, gentle) in a safe and familiar setting?

For what it's worth tonnes of kids are terrified by dogs (I was as a kid too). It was bad enough to be a serious fear that stopped me enjoying things like going to the park. In hindsight I wish my parents had done something about it (even as simple as just talking to me) but they were not at all tuned into my emotions or needs or inner life, shall we say. I'm not suggesting my experiences were like your kid's tho.

As a dog owner I always try to notice this and keep him away but there are times when I feel pretty bad, even just walking him on a lead on the pavement you see kids cower away sometimes. Not sure how it's possible to avoid this though.

My dog has done this.
And I am sad and disappointed it has happened.
You are right to look after your son, full stop. You don't have to batter the dog when it approaches you. Just grab it by the collar, stay calm, and wait until the owner comes up. If you can do all this while your son is understandably upset you are a superhuman.
You can tell them exactly why you're doing what you're doing, words like "someone should have the dog under control and I thought I'd try" (@Constable_Savage for the quote).
And then you can explain. And then you can leave. You don't have to give any further explanation.

Unfortunately, it will happen. But it's not up to you to try and plan for everything. You're right the law is there for a reason.
I think tower Hamlets are looking at changing/enforcing better the rule and making it "lead on" all the time because of situations like this with bigger dogs. Which means, it'll probably happen london wide at some point.

I'm also going to guess your son's normal reaction to something running up to him that is not wanted probably whips the dog up a little bit.

Obviously, I'm responding from a place of "i've been that dog owner (but not the one that says "oh she's friendly!")" .
If my dog is on a lead, I'm very mindful (and demure..) of who is around and who is nearby and what they look like they're doing (are they scared, are they taking a wider line , why are they walking over to pet my dog?). And when she's off lead I try and pick a place that she will only be interested in what I'm doing. Obviously, there are times when this hasn't worked ("is that a dog 200m over there!? FUCK YOU I'M GOING THATTAWAY").

Any thoughts?

Well, we don't know your son. 'Autism' is a very widely-cast spectrum that captures completely different people. In general, dogs are thought to be congenial to many autistic people—while they can be exuberant and boisterous, especially when young, they are also faithful, constant, affectionate, and uncomplicated. We've just heard from @GoatandTricycle about their autism assistance dog.

Again, we don't know what might be possible to achieve for your son. He may need some habituation to dogs, as lemonade says. He may need to learn that dogs can be friendly even when they bark, that they are often just happy to sniff his palm and that they generally don't bite. If you can do anything, it should be gradual and not include sudden surprises. If this works with him, it will address the problem at source, and he'll know what to expect (very important) when there are dogs around. Also, many children are scared of dogs, and it certainly isn't something confined to autistic people. It's quite normal.

I think if you can find a calm dog to try some desensitisation you’ll gauge pretty quickly if that has any mileage. This can work but I also know there’s absolutely no way to overcome some of H’s challenges with traditional approaches like this.
Is he verbal?
Where are you based?

We had the opposite H wanted to say hi to every dog and that lead to some awkward dog handler interactions.

So you could carry a lead, you could then take the dog away from your son. Probably going to annoy the owner, carries some risk like grabbing the collar from the dog too.

Carry high value dog treats. Scatter to distract dog away. FYI these generally stink, little cubes of cheese could be the simplest solution.
Could be paired with sit as most will know this command.

Another tip is I use makaton regularly in situations to flag to others that H is “different” even if it’s not really needed. You could do this if you have hold of the dog, signing to your son.

Whoops, should’ve read the thread updates before joking about scaring kids, soz.
I take our terrier on the school run via the local park and there are a few kids who are clearly scared of off-lead dogs. Always put him on a lead when I spot them just in case he wants to give them his ball, just like avoiding Alsatians etc. Very tricky to control random sniff events though, when my son was small he had big dogs in the park jump up at him, albeit playfully, and I’ve ripped the owner a new one.