Yes, but it's good practice, at whatever airport where your BA flight goes from, to check at the lounge that they have registered your bags through to the destination from the inbound flight. It isn't a fail-safe or indeed absolutely necessary, but it is a good idea. At LHR (if that is your route) then ask the agent half way down the airbridge just before your board your final flight to see if they have the information there about your bags. Depends on airports, some airports are better than others.