I'm another example of not getting a degree before becoming an ATCO. I lost count of the amount of people on my course (Course no.83, yep, I'm an old bugger now) who had degrees and ended up out on their ear during the training phase. I started when I was 21 after spending three years fannying around working in a pub. Do what you feel is right for you, having a degree won't hurt, but it won't necessarily help.
Anyhoo, my best mate at school went to uni and got his degree in Geography. He's a foreman for a construction company now (Whitemountain/Lagan Group, the ones who do a lot of the runway re-surfacing in the UK), but he started off with them mixing concrete. He's been at it as long as I've been an ATCO and earns half of what I do. Mind you, if it's a Geography degree that you really want............