I dont think you have to have read books. It obviously helps alot but I think alot of people pick up a love for reading as they go along. I would recommend reading as much as you can over the year in your spare time.
Whilst in Uni you will have to read about 2 novels a week, sometimes more. You are going to need to feel comfortable with this level of reading or you will get behind.
Personally, I have always lived and breathed reading and literature. I love it, and so had a lot of my course friends. But so many people on my course had never read that much in their spare time.
Knowledge of the classics will get you far. During my studies there were so many times when I would think 'Oh that links in with this book' and 'ooooh i can see how that can be compared to this...' and it helped me in my essays. The more you read and love literature the easier it is.
I would also recommend reading some of the introductions to the classics as they give you an idea of how critics interpret certain texts. I remember having quite an exciting moment reading the Intro to A Clockwork Orange and Lolita and thinking, YES this is what I want to do I love the way people write their responses to novels. Geeky but true.