Tom Hunter,
I get the impression you are relatively young, am I right?
Arbitrageur is right. If you are successful in obtaining a stint of work experience use the opportunity wisely and network appropriately. But don't run before you can walk. Finish your education, degree subject selection isn't anywhere near as important as getting excellent A-levels and picking the best university you can.
It's the institution that your potential employers will look at, (and the grade on the paper), not so much the subject. I have friends who are in banking and trading and they studied history, biology, classics at uni, not economics, stats, maths or business, but they got all got upper first/upper second class honours.
As NQR articulately stresses-"HARD WORK+GOOD EDUCATION"
Therefore, pick a subject that you like and that will keep you stimulated for 3-4yrs, try to make it something you are good at and if at all possible do an 'old fashioned' degree at a red-brick Uni, e.g. Biology at Nottingham or Economics at LSE.
One other thing, sports, leadership skills, being a confident individual, good social skills, looking sharp are all important too. Stay healthy physically and mentally and don't let the concept of hopefully being a trader one day take over your life, that's not healthy.
A good friend of mine who happens to be an investment banker at JPM has given me advice ever since I started Uni in London and I'm quite happy to help anyone who's keen on learning more, read the following list of books, nothing too heavy, but I'm confident that you will develop a deeper understanding of trading/traders. Develop yourself personally as well as academically, interpersonal skills are crucial!
Liars Poker-Michael Lewis.
Trading In The Zone-Michael Douglas
Reminiscences Of A Stock Operator-Edwin Leferve
Once your at Uni, think about taking the odd professional examination i.e. The Securities and Investment institute Unit1,2,3 papers. This will show willing and initiative.
Generally read material which comes recommended like the above.
You seem to be in a good position at the moment, organise yourself well and strive for excellence in whatever you are doing and you'll give yourself the best possible chance of meeting your objective.
*Just a brief personal note: I was in the same position as you at one point, after all I've done so far one of the best things I can recommend is to take a gap year before uni and go travelling and see the world.
Best of luck,
STH.