I'm a third year maths student at a top university who is in the process of applying for MSc's in Aerospace related subjects.
If I were you, if you're serious about going into engineering afterwards, I would advise you now to think twice before going ahead with your maths degree.
I was in an extremely similar situation to you a couple of years ago; I was constantly told that it would be possible for me to go into engineering afterwards. To be honest I wasn't lied to. It is possible, it's just difficult.
Like some people here seem to be saying, while a maths degree will give you the maths and problem solving skills to be an engineer, if you ask me it will give you little else. How in your course have you obtained the teamworking skills, the communication and management skills, the project and practical skills? I have a problem right now answering these very questions on Masters applications.
Of course a lot depends on which course you're on, and which modules you take, but in general, I think that's as much as you'll get out of it. I'm probably being slightly bitter as I have not really enjoyed (or done particularly well on) my maths degree at all: I got tired of the so called "beauty" of the pure maths, and the applied stuff hasn't been taught well and is normally done with outside departments.
Outside of finance, mathematical research and teaching there are very few technical (i.e. uses maths/physics) career options available to me that don't require a further postgrad qualification.
I strongly urge you to rethink your degree and career choices bearing this in mind; apart from things like specialist finance/actuarial roles, and mathematical/theoretical physics research or teaching, I don't think there's any career path closed off to you if you decide to do engineering. Ultimately the skills you obtain from an engineering degree will be more appliable.
Also, if this applies to you, PLEASE don't use your "interest in pursuing maths research" as the main reason for undertaking a maths degree, if anything remove it from your reasons and consider whether you'd still want to do the course. I got what was the equivalent of A*A*A* at A level, a 1 in STEP I, and a Distinction in the Maths AEA. Pretty soon I realised this means very little once you start uni, and is in no way evidence of your ability to pursue the subject at research level. Maths at uni is a completely different ballgame, where until you actually do the modules, its difficult to determine whether you'll enjoy them and perfom well in them.
If you do decide to carry on with maths, I'd suggest you go to a university which also has a decent aerospace department, so you can switch in your first year if you change your mind, and so you can also possibly take modules from the engineering department.
If you're interested, the MSc aerospace subject areas available or relatively easily accessible to maths grads are predominantly in Fluid Dynamics (more Computational than Experimental of course). I may also take a shot in applying for propulsion and thermodynamics related courses, though even this will require a considerable amount of catching up IMO. Funding is also something to bear in mind. You will not be automatically entitled to any government funding, which may result in you having to fork out something in the region of 10-15 k to cover mainentance and tuition fee costs, or borrow from a bank. There are scholarships/bursaries available, but you apply for them only after recieving the offer for the course. In other words, you can't really assume you're going to get any funding.
Finally, having attended various aerospace related careers fairs, I'll tell you what the employers seem to say. Many say that they are happy to accept applications from maths grads (assuming no MSc), but they'll give favour and priority to the engineers. In today's competitive job market, this makes securing a job almost impossible. Pretty much all of them agree on the fact that I'll improve my odds (and knowledge) by doing a Masters, which is what I'm doing now...
EDIT: Sorry didn't see your final question. Yes there are other jobs in aerospace firms, such as finance, purchasing, logistics, etc. All of them are a lot more stats oriented than physics/engineering related though. Any other questions PM me