You can do this AA-to-BA because unlike other carriers, AA will protect you across separate tickets AA-AA and AA-OW (as well as OW-AA on the return). However, as you have pointed out you must allow the time collect your bags, lug them to BA, check in as though originating at LHR and proceeding from check-in.

The only thing you forego here is the need for more ground time at LHR.