From what I understand... If bags are loaded at LHR under BAs control, they make no difference. My bag is pretty much always one of the first 10-20 bags... Today I picked up my bag at LHR after doing 3 flights in Asia, last one BA First SIN-LHR, and it had a First sticker... didn't make any difference whatsoever. At least 40-50 bags ahead of mine. Think it depends mainly on what airport your bags get loaded at, but happy to be proven wrong