I was in the same shoes as you couple years ago. After which I enrolled in Part 147 organisation where I am taking my Part 66 exams. If you think Aerospace was hard..wait till you do these exams! - not mathematically as challenging but a tight schedule and high pass mark really puts the pressure on.
Graduate schemes are good and most people who do work in the airline industry tend to do their exams privately (CAA Exam centres) or an airline would normally run the course internally which means you could take the exams while you work!
This in itself is quite hard as the work load is alot and i cannot imagine doing these exams while working,not to say people havent in the past.
So I would suggest, you enrol yourself in a two year course and do the exams before looking for work. As I am finding out, alot more companies will be happy to interview you.
You will be working for the rest of your life, so do all the exams and get your stuff together before your look for work.
Good luck.