I'd also recommend Riley, Hobson and Bence, which has all the benefits and disadvantages of being bigger: (http://www.amazon.co.uk/Mathematical-Methods-Physics-Enginee...)
For A-level, most students I've taught want me to follow their school course, so I've mostly taught out of an array of textbooks of varying quality. On the whole, the standard A-level course books for EdExcel, AQA, OCR and the like are adequate, but only really as part of a taught course. If I cast my mind back, Bostock and Chandler was quite good, although I suspect it will be a bit retro by now with respect to syllabus changes - it was old when I was learning this stuff for the first time. That said, mathematics is one of the more stable subjects and the fundamentals don't change very much, so I'd definitely recommend looking at it. Obviously, if you're not looking for something to pass an exam with, classic books become a lot more appealing.
http://www.amazon.com/Mathematical-Methods-Physics-Engineeri... (click to look inside -> table of contents)
The "other world" that I'm much less well read in more involves proofs and foundations, and would probably start with Euclidean Geometry and Set Theory, then topics like Abstract Algebra, Topology, Advanced Calculus, Real and Complex Analysis, Category Theory, and so on.
I'd also recommend j2kun's blog, which I've found great for a first intro to many topics, though it has a bit of a programming focus: http://jeremykun.com/ As mentioned above, Khan Academy, Coursera, Udacity, EdX and the others are good too, especially since they're free, so you don't have a lot to lose if you get in over your head.
Not sure if this will help, but it can't hurt.