The trick is to do your online check-in precisely 23 hours and 59 minutes before departure time. You should stand a good chance of getting a seat in row 28 or 29.
Incidentally, as a Blue EC member BA will normally pre-allocate a seat, and I've found that usually it's in the 28/29 range on the 747s. What I find slightly galling is that when travelling on a cheapie, I am always allocated a window seat when my profile clearly states Aisle, but if I'm paying full fare I get the aisle allocated. There's a subtle hint in there, I think.