There's a bit of confusion here.
, that is to say, a BA flight operated by a BA crew, aircraft & with full BA service (aka BA 'proper'
), stopped flying to THR a while ago (I don't know exactly when).
The route was dropped, probably because it wasn't making BA any money.
Now, Bmed comes into the story. They are a MUCH smaller operation, specialising in serving 'niche' markets with appropriately-sized 'niche' a/c (the A320, and soon, A321).
Because of this, it is much easier for them to turn a long, thin route (such as LHR-THR or LHR-ADD), into a money-earner.
BA would like to continue selling tickets to places such as THR (whilst also including the destination on the 'BA' network), without incurring the cost (and losses) involved with actually flying their own a/c on the route.
I don't know what the exact arrangements are, but obviously BA pay Bmed to fly their a/c in BA colours, and offer, essentially, a BA product on-board.
Bmed gets the cash from BA, BA gets the cash from it's customers-or something like that.
Anyway, the point is that BA stopped, Bmed then picked the route up-I don't think there was a situation when both flew the same routes simoultaneously.
If anyone knows any better, I would be interested to hear!
Here are BA's franchise partners: