Pete, unfortunately the only thing that matters in BA is seniority, and there's nothing that will get you anywhere faster(except becoming senior management, but dont go there!). That said, a number of ex-mil guys have told me that life at the bottom of a long haul seniority list was miserable. The A320 is a rapidly expanding fleet, and fast moving in terms of seniority. Two years seniority would see you very comfortably placed with the ability to get a preferred choice through bidline, provided you bid realistically. The A320 is not yet a touring fleet like the 757, and 5 or 6 'mini-tours' is unrealistic at the bottom, though it may be possible to minimise travelling to LHR if you're prepared to spend a few nights each month in a B&B there.
On the question of command times, LHR is very much the jewel in the crown of BA and will always have the longest time to command. If early command is important to you then I believe it can be as low as 4 years at Gatwick, and also quite low in the regions, although that may change due to contraction at MAN. Its worth bearing in mind that its best to become a BA pilot rather than an FJ pilot before gaining a command. There are a few people around who haven't seemed to shake off their single seat idiosyncracies, and they're a pain to fly with!