In essence, there is no such thing as standby in most (all?) of Europe. For BA services it's kept for staff and irrops essentially. So if you managed to get through T3 quickly - and 1 hour is both the MCT (depending on precise circumstances) and an adequate connection time there - then there are only 2 ways you can go earlier: (1) if you ticket allows changes then you can do the change at customer service desk in the T3 lounge (Galleries Club, right next to Flounge, just after reception on the right). The cost of this depends on your fare basis. £60 plus fare difference isn't usual (2) if there some sort of event - e.g. bad weather - where it suits the airline to get you out of the system quickly. Even for that, BA can be fairly slow to cotton on to a problem.

So if on one ticket, the best thing to do is to book for the minimum connection possible. If you don't make it then they'll transfer you on to the next flight, the only risk being if that later service is completely sold out.