On the basis that FlyBe paid compensation out to me last summer when the flight before had a technical fault at the up-route airport, I'd say it's poor form of BA not to pay out in these circumstances.
I seem to recall someone from the CAA (in a BBC interview) saying that if it was up-route, then the airline had no defence.
Maybe BA are just trying it on - 90% of people will just walk away here. Call them on it and say you believe that comp is payable, then either refer to the CAA or issue a letter before action & go straight to a small claims court.