My advice when treated like this is to get Small Claims Tribunal (or whatever lowest cost option is available in your jurisdiction) statement of claim forms, fill them in, send copy to BA (or other organisation treating their customers like scumbags) saying "if I don't have a response to my satisfaction by (2 weeks later) this gets lodged".
Works like a treat. They may come back to you saying that their small print excludes liability in which case you say "there is every possibility that you may rely on the small print, but I am going to make sure that the scumbag way you treat your customers is known to the widest possible audience".
BTW don't mention compensation or you may get a visit from the boys in blue (demanding with menaces).
I have used this technique to get the business class ticket I wanted on my airmiles (airline couldn't offer me ANY options many months in advance though I gave them a huge window of flexibility), so I sued them for the full price of the fare in lieu of the airmiles. They called me to say a seat had been released on my preferred choice of flight.
All it takes is a bit of time. Basically they hate ending up as a tail piece on the evening news.
HKPAX