I would suggest that you should be able to select the best hospital for your needs. The normal expectation would be that you’d see an MS specialist if one is available. But assuming both hospitals are within the same NHS Trust, and they both have neurologists, you should be able to self select.
I see a neurological rehabilitation specialist in one hospital, a neurologist is another (which is outside of the Trust area - there’s an understanding that the neurology services at that hospital are best for MS). I also see a urologist in one of three hospitals within my local Trust (for some reason the venue changes from one appointment to another) and a colo-rectal specialist in my preferred hospital. I also see an ophthalmologist in yet another location within the Trust. So basically, I’m seeing different specialities in many different locations. Often it’s my preference that drives the location, sometimes it’s the specialist unit.