I applied to Bath in July, and was studying in October the same year. So, if anything, January feels rather early to be applying. I think that was through UCAS, though I called the university first.
As such, I think I'd advise spending a month or so working on academic subjects. Guessing whether you'll love a subject or not without reading it is pretty much impossible. It'll be rough going, but it gets easier, and it'll be a fairly strong indication as to whether a degree is a good idea or not.
I'd recommend Algebra and Geometry, by Alan Bearden, as a friendly pure maths book. The other option are the analysis textbooks, an interesting field, but I think less approachable.
For physics, comp sci, engineering etc, you can't go far wrong with "Mathematical Methods for Physics and Engineering", by Riley, Hobson, Bence. Success in the physical sciences pretty much hangs on how competent you can become with mathematics, so if you can make sense of much of RHB, you'll be fine. I haven't met a physicist yet who isn't interested in the subject, but I've met a lot (and am one) who fell over at the mathematics part.
For physics itself, find a copy of the Feynman lectures. They're unmatched for undergrad physics. If these don't inspire an interest in physics, nothing else is going to.
All the books listed are readily available in libraries, through disreputable websites, or through amazon. Best of luck.