That's because you can't fly between LHR and BHX. Birmingham to London is less than two hours by train city centre to city centre, so it's just not a journey people would consider making by air unless they are connecting with a long-haul flight. I know there used to be flights on that route, but I guess they proved to be commercially unviable - the same as flights from my nearest airport (NWI) to LHR which were discontinued about 15 years ago.