I came across this blog, which is both interesting (as an able bodied person) and I suspect very useful to ellie_nz. It provides a lot of lines of approach that can be followed up. I suspect the writer is a FT contributor too.

Kiran's Blog - Heathrow

An additional point: I mentioned above how EU261 may not apply, but it occurred to me that in fact there are a number of clauses in it stressing the needs of those with reduced mobility. Seeing how the law works in other areas, this typically drastically lowers the bar on any defence BA may invoke. I can see they just about fulfilled section 11.2 below, but failed on clause 11.1. Firstly in not responding adequately for the plea for a wheelchair close to departure, and secondly letting the aircraft depart knowing that a wheelchair passenger would be shortly getting to the gate.