change to maths??

hi everyone, would really appreciate any response. I'm a year 12 currently doing history, politics, english literature and fine art. so far, the courses on my possible list are history, history and politics, and hsps at cambridge...but since reading a few books I've started to like the idea of economics so am now considering ppe. But of course, I would need maths a level. I am good at maths...I mean, I was one of only 22 people in my year to get a 9 last year. I also enjoy it, not as much as my other subjects, but I found myself mildly missing maths when looking at my friend's work whilst studying with her the other day. is it too late to change now (unfortunately, I would be dropping art in exchange for it)??? my school's official deadline to change was a couple weeks ago but they have been known to make exceptions.
Alternatively, I know oxford DOES consider applicants to ppe who haven't done maths a-level. is it worth it to apply to oxford ppe instead of cambridge hsps?? considering I have wanted to go to cambridge since I was a little girl.
Or, as a second alternative, can anyone convince me that doing a non-maths/economics related degree will still put me in a position to have a successful career? - this is something I have been worrying about, especially in a very academic school where EVERYONE wants to be an engineer, dentist, doctor or in finance. I am not stuck on a particular career path just yet but would like to travel, meet and help lots of people, be intellectually stimulated and be comfortable financially. I'm also not completely against doing a law conversion though I am aware of the cost.
Thank you! sorry if any of these questions are silly...