This is fantastic news ... I was a big fan of the BHD-LCY route, though always torn each time I booked onto it because it meant another FlyBe trip.
I had the impression that the BHD-LCY traffic wasn't a big deal for the BHD-LHR operation bearing in mind that BHD lost LGW services from both EI and BE in recent years.. The complementary BHD-LHR service from EI may have influenced the BA schedule more than the competing BHD-LCY service.
Though I am definitely pleased to hear that BA are filling this gap.