The whole idea of BA operating cushy routes out of LHR with no competition is a (Branson-perpetuated) myth.
Take Sydney. The Bearded One screams about a BA/Qantas 'duopoly'. Well, fair enough, if all you care about is getting off at SIN or BKK and back onto the same aircraft.
Anyone else can see that on LHR-SYD, BA competes with CX, SQ, TG, EK, GF, JL, soon to be QR and many others. They all compete on a value/service proposition.
Across the Atlantic, the competition is fierce.
Even the Gulf, a goldmine for BA, has extensive competition from local carriers.
I think the only BA route without competition is Bermuda, and in King's word's, there's hardly enough for one....