There is no need for them to fly to New York City. Both British Airways and Continental already fly the route non-stop. They are also a Star Alliance airline, and both Washington Dulles and Chicago O'Hare are Star Alliance hubs. They have a very small long-haul fleet and have to carefully use their long-haul planes.
As for other destinations, bmi actually was planning on starting non-stop Miami-Manchester service last winter, but American Airlines decided to start the route, and bmi held off (there is not room for two carriers on MIA
), and went to the Caribbean and Vegas instead. bmi had also looked at serving Boston, but, again, AA