The aforementioned free car-park is the visitors car park for the Cranebank Flight Training Centre... its on your right just b4 you get to The Rivers (in the Cranebank complex)... signposted fairly clearly.
A slight caveat however - since BA don't tell the wannabees about it, I'm not sure they'd be completely overjoyed with every wannabee using it - I know about it cos I've used it as a visitor. Saying that, you could argue that CEP applicants are visitors as well (and it certainly beats relying on public transport to get there!).
Hope this is some help...
RS.