This is what's actually bothering me. I would love to do Aerospace and get in with the likes of Agusta-westland or Eurocopter, but I'm sure the likes of a Maths Degree would still get me on the Graduate Programme they run.
To be honest, probably not maths.
Maths tends to lead to relatively "back room" jobs - Aero-Eng on the other hand is regarded as a high quality general engineering degree. Aeronautical engineering grads seem to end up just about everywhere.
If engineering interests you, and you're really concerned about becoming over specialised, then I'd recommend mechanical or electronic.
On the other hand I'm a chartered mechanical engineer (as well as aero) off the back of an aerospace engineering degree. I have friends with the same degree, from the same university who are variously RAF and RN officers, a schoolteacher, running half of parcelforce, and a recently retired bank manager. Oh yes, and quite a few professional engineers, and a number of professional pilots - including quite a few test pilots.