Although this appears to be a dissenting opinion, I have never been drawn up by BA in relation to my excess baggage. I have often travelled within Europe with up to 30kg on a 23kg limit.
Now, my experience might have been influenced by the fact that I have status, I don't know. I think it is also affected by route. The BKK/SIN Oz routes, spring to mind. I suspect the reason for this is that the impact of the excess baggage on board has a much greater impact on fuel consumption. On the shorthaul routes this is less of a problem.
bealine is probably the best person to express a view as to what you might get away with.