It is a tough one.A lot of web designers are self taught to start with a can fall into it really.
Obviously, a strong IT/Design/Art background will set you right. You can choose to got to college/uni and either go with a graphic design route and specialise later on, or go the web route from the start.
A quick search of UCAS shows that there are the web design/development road or the multimedia digital designer road. The one thats most appealing to you is best, but bear in mind to keep your options as open as possible.
Generally most of the courses here seem to want 2/3 A levels (normally one in a related field) and around about 200 points on the new system.
Best bet is to decide what exact route you want. Do you want to code stuff? do you know CSS/HTML/XML blar blar blar? Is making working websites your thing? Or do you prefer multimedia flash websites?
anyway,
here
should help