scroggs is absolutely right! I know lots of guys doing Aero Eng and many are itching to get onto the flight deck, having not yet finished their degrees. Saying this, degrees as back-up qualifications are a good idea if you don't have a good set of GCSEs and A-Levels behind you. If you do, however, have these good results which you could use should (touch wood) something medical happen to you down the line, then why not go for sponsorship now!? BA may cease the cadet pilot scheme by the time you graduate and they do have the largest intake of cadets with no money upfront. Personally if you LIKE aero eng then start and go for all the sponsorships you can, but be ready to leave if you get one. If you just want to be a pilot and were going to use aero eng as a route into flying don't bother- the course is very hard work and long when there are other easier routes into the flight deck.
Try doing a search on this website for information (use keywords and the wannabe section) and you'll find it amazing how much info and debate about this there is.
You don't need a degree to fly and if you want to risk the whole medical thing then fine. But there are three people starting on my BA ATPL course who don't have a degree!
GOOD LUCK!!