University Maths topicsWatch
Number theory and set theory/logic are good introductory topics. The fundamental ideas of set theory/logic pretty much underlie mathematics.
If you know/like calculus - you could look at vector calculus, real analysis (in which you pretty much restart your study of calculus and spend far less time doing calculations) or deeper into the qualitative theory (ie. more concerned about the behaviour of solutions rather than finding them explicitly) of differential equations. Complex analysis can also be tackled, strictly speaking, just with A-level complex numbers knowledge (bar possibly some missing vocabulary from topology, texts may assume varying amounts of familiarity with real analysis) but is generally not met until the second or third year of a maths degree.
If you like probability you could look into covering probability from its foundations, but eventually you'll need some real analysis. (you should have a grasp on bits of set theory too)
University maths is quite different in style to A-level, bear in mind, it will seem a lot more dense.
Personally, I'd have found gcx's list far more palatable than BMO/IMO stuff, but everyone's mileage will vary.