I was about to ask that, VK. I thought BAA was responsible for the bussing rather than BA, but, of course, most passengers just equate the one with the other and the blame gets shouldered by the airline. It’s true about LH. They manage rather well, at least that’s been my experience. Series 7 door to door.
Certainly agree about some sort of better transfer for f pax. at T5 when it’s necessary.