Not BA, but flying Business with Delta, I remember the CP (or whatever they call them) trying to reseat me from my window seat (with free seat next to me) to an isle seat in a fully occupied 3-seat middle row in the forward section (B767) "for my convenience". I refused. He wasn't happy and showed it. Talking to another member of the crew I learned that he was trying to section off a part of (the not full) Business Class cabin as the crew rest area!