One World is spread over T3, T4 and T5 at Heathrow. I'm flying out of LHR on MH (from T4) next month, but will have to connect on a different ticket (my plans are being finalized) most likely from AMS. Given that KLM use T4 I'd choose them to make my connection easier. Previously I'd have used BA. It really isn't a well thought out Alliance any more....

Or perhaps this is just a move to ameliorate the problems of expanding Heathrow. Given BA's dominance, and One World's reluctance to help travellers make connections, perhaps people will start using airports which are hubs of Star Alliance and/or Sky Team to make their connections in Europe. LH and its subsidiaries are the obvious beneficiaries.