You don’t need to prepare anything special for most British colleges (aka “unis“). Some have a special math test so if you don’t take it you won’t qualify for these but otherwise all you have to do is go to UCAS, list all of your GCSE results, AP scores, etc (= external examination results), choose 5 “courses” (programs), explain what makes you qualified for math/stats studies (“personal statement”), have a Math teacher upload all the ways in which you’re qualified to study Maths at the University level (“reference”) and that’s it.
Wrt rain, if you stick to Edinburgh, East Anglia, London, Sussex… it would be okay and MUCH less rainy than Oregon/Washington state.
With your AP 5s in Calc BC and Physics 1 plus relevant APs I’m willing to bet one of the non exam universities would offer you an unconditional place for Maths/Statisticsby December.