BA will have to order something new for longhaul in the next couple of years. One rumour suggests the 747 Advanced, although I think a combination of 777-300s and 787s would be more likely.
From an Airbus point of view, it would presumably be some combination of A340s, A350s and A380s. Personally I think that's unlikely, although I would expect to see a few A380s at some point.