A look at LinkedIn would appear to show that BA would appear to recruit quite a diverse bunch onto the programme. Bear in mind that when you turn 18, you've got at least a 15 year, possibly a 20 year window in which to apply for these programmes. Some do get in at 18, though at BA it wouldn't appear to be particularly common.
I'd say Maths, Physics plus something else at A-Level, keep doing the DofE awards, potentially get involved at your local gluding club as a "cadet" member.
Lastly, remember that whilst BA have offered a very good programme, be aware of what else is out there too. Aer Lingus offer a programme that doesn't involve a loan, the airline pays everything. I came quite close to getting on it and I know a bloke who at 19 came close also.
Finance-wise, things would appear to be a bit better than in say, 2006. Airlines seem to have cottoned-on a little bit to the fact that not everyone has rich parents, so take a discerning view.