Speaking from recent experience, I certainly wouldn't rely on BA for disability assistance. So far in 2014 my other half and a close friend have both required it on separate occasions due to injuries and both have ended up abandoned in T5, with their respective flights ending up delayed whilst lounge staff tried to find out where their wheelchairs had gone.

I don't know who BA contract to provide wheelchair assistance but I'd use another airline if they're going to struggle to get about on their own.