It's quite a long story but basically BA didn't stand in the way of bmi's acquisition of BMed on condition that bmi sold the Heathrow slots to BA over a period of time. Most of the original BMed slots are now held by BA and bmi continues to fly the former BMed routes plus some of its own expansion into similar territory using slots which it has reassigned from routes like LHR-CDG, BRU, AMS, MME, LBA that it no longer flies.
BA was only interested in the LHR slots. That will undoubtedly be its main aim this time round as well.