The sixth form at my DS's secondary only did the ICT Btec so we hunted around and found a college further away that did compsci A-level (along with maths and FM) and now he's going there and have to say we're really glad of it. His friends who stayed put are frustrated with the Btec as it's very 'IT' with little programming and not stretching the bright ones. It would be fine if they wanted to go straight into IT office jobs but they've started to realise (later than you/your DS) that it's not going to count for some unis in the way three A levels would. That's okay, as you've sussed, for places like Goldsmiths where it's not a mathsy kind of compsci and mainly about the artsy application, but it sounds like your DS is like mine who isn't so interested in that side of things and wants the more hardcore compsci, digging into data and things that are frankly beyond me!
I get that he's set on the small school and you've done your research and of course his happiness is vital. That said, my DS is ASD and I've been surprised and impressed with how he handled the change, mainly because he's fully focused on studying and not bothered about the social side of sixth form. It depends on the nature of your DS's sensory issues, but I wouldn't assume a huge sixth form is necessarily going to be full on noisier than a smaller one just because there are more kids on roll. The class sizes will probably be similar and he'll only be in the classroom or the library for most of the time. Plus unis are big, especially in London, so if you think he could cope with UCL or Imperial, then arguably a large sixth form is better preparation? And keeps options open.
I'm not at all anti-Btec and think my younger son might well do one in his artier subject, but I just wanted to add my experience here because the ICT Btec specifically seems to be a very different beast to a compsci A level, and if he wants to do compsci at a high level, then he's arguably better doing three 'straight' A levels (e.g. maths, physics and FM) plus his own programming on the side, than doing the Btech just to have a CS qualification only to find it's unhelpful for uni and potentially frustrating for the next two years. There's also the shortage of CS teachers of course which has led to the lack of CS A-levels, but a side-effect is that some of the people teaching the Btechs are more like business studies teachers who can do ICT as opposed to the CS teachers with maths backgrounds, so again, it becomes about office-based vocational ICT, which doesn't sound like a great fit for your DS as it isn't for my DS's friends.
Again, I'm aware you've done your uni research and if he's all good to go to City, South Bank or have a crack at the 'top' ones who say they take Btech (might be worth asking how that shakes down in reality), then stick with the sixth form of choice. But just wanted to mention all this having been through it all recently, and now going around to uni open days and seeing how very different CS degrees are in different unis, I'm feeling relieved we took the gamble of going further afield and giving him the most options going forward. Good luck with it!