The PP is wrong about people on UC not having much luck with the social housing here. Virtually everyone who applies for it will be on benefits.
I suppose there are registered social landlords that are private individuals and they'll be like any other landlord and not want people on benefits really (which is discrimination if the family have a disabled member of course, but that's by the by.)
But things like housing associations will be mainly applied for by people on benefits (though I know HAs etc like to try and have a mix of people.) get on the list/apply for absolutely everything.
@Akkhan94 I think if you private rent what you can afford, you could probably still stay on the council list as band C overcrowding due to needing more space than the average family because of your son's disability.
The thing with agenesis of the corpus collosum as I've understood it in the past from reading, is some people with it have no extra problems than anyone else whereas some will have major problems. So you have to demonstrate the level of impairment. If you get DLA that will help prove that.
I got an ok private rental in the past which was previously a council flat and the estate agents were laid back about who they allowed there for that reason (I'm disabled and unable to work pretty much for that.)
Other places you can private rent @Akkhan94 are over to the North of town I think. A lot of places there are cheaper. City Road etc etc. They're not the nicest of areas but would be a space of your own.
Nothing anyone's said is about your surname having Khan in it BTW. Seeing as how we're not psychic and wouldn't know what your name is. 
I think a lot of us understand that Asian women sometimes end up in this cultural family set up, but most of us would have nothing but empathy for someone in that situation, because we can only imagine what that situation might be like, and even imagining it sounds hard work enough, unless you happen to have parents in law that are actual saints, and even then it'd tend to be more cramped than most of us would enjoy.