Yes there are classes for you. Of course its very expensive to get going. Buying a used kart and tools and racewear is gonna be around 3000-4000£ so you will have to show your parents you really want it.
You really don't need that much if you just want to race karts without owning your own kart, I've been racing in an arrive and drive league at my local track since i was 8 (now 17) and it isn't particularly expensive, doing the winter endurance rounds at the moment me and my team mate split the £90 bill between the 2 of us and that's an hour's race and 15 minutes practice and 15 minutes qualifying. If you look around enough it doesn't have to cost as much as you'd think.