Oops, I skipped a line and thought you said you couldn’t take BC until senior year, not that you couldn’t take it at HS at all. Yes, you really need a strong math background for a real CS degree; there are some less demanding course which are not CS but called things like Computing or IT which you could get into. But if a British university wants Maths A level for domestic applicants, you need Calc BC AP.
Can you clarify: are you specifically looking at CS and Business combined/joint honours, or open to either one area or the other; and what about CS appeals?