Usually an overnight stay with an early flight the next day. You can proactively ask to go to AMS (for example) if you wish, but the tradition there is that you are then on your own, you can't then ask BA for the train fare down to BRU.

BA do sometimes re-route on to other airlnies, certainly JBA and some European airlines, but that tends to be offered as a last resort really, and it helps if you have status or on a premium fare.