2 little corrections to things said in here - the A350 is offered with GEnx engines so far - at least to my outfit. We have NOT been offered a Trent 1000 powered version, suggesting GEnx is the only option (at least up to now).
And whoever said Blanc was head of Airbus marketing was making it up. Blanc's in charge of their program department, not their marketing organisation. Believe that title lies to an American chappie (which is impressive considering the French dislike for Americans at the moment....).
As fror the main question - the 777-200LR and -300ER are only available with GE90s - something which has stung BA before. Now hopefully the -115B is a well sorted engine by now (it had big trouble at EIS with Air France) and I don't really see where the -200LR would fit into the network. The -300ER, though, could well be a good fit and seems to be a very good airplane these days (now the CG issue is sorted out a bit better).