If flying AA and you connect at LHR to your BA flight, you will likely need to exit security, claim your bags and recheck them at BA T5 (assuming your connecting flight departs from T5). How much time will you have to connect?
Would both of your BA flights be on the same reservation? If so, then you should be able to check them all the way to your final w/out having to exit security; if not on same reservation, there is a possibility that at least you won't have to change terminals.