Hello!
I'm a current first year at the LSE, and have had such a great experience with the disability team (which I didn't expect tbh!!). I'd say that it's worth trying to get in contact with someone from the disability team at the unis that you are considering, as support does vary a lot across different institutions and courses.
In terms of support that I received (with physical disabilities and neurodivergence), I got loads - recorded lectures, no penalty for not attending class (as much as possible), all class/seminar/lecture notes in advance, access to rest rooms on campus, deadline extensions, a locker in the library, and exam adjustments. Basically, I got everything I thought I would need and more.
I would also really recommend applying to DSA well in advance of starting uni - I left it until Christmas of this year and was very annoyed at myself as I realised how much better I found uni after recieving this support.
Hope this helps!