Well firstly, grad schemes at the top accountancy firms will train you up and have you sit the exams to become qualified in the first 3 years anyway. My grad scheme has me on the ACA, and expecting me to complete in 3 years since starting. The typical route for a grad scheme at Big4 and middle-market firms (RSM, BDO, GT etc) is Associate for the first 3 years (complete the ACA in this period), then upon qualifying move to Assistant Manager (typically with a pay bump to around 45k-55k). After that it likely takes 2-3 years (very dependent on your competency and relations with the more senior managers) to become a Manager and then a similar time span and requirements to make Senior Manager (hopping across firms can speed this process).
As far as your subjects go, pick PPE if your interested in it and would find it fun. A friend of mine who I met after joining came from a Music degree. Doing an Accounting related course can grant exemptions from certain ACA exams (my firm allows me to take exemptions and since I did an Accounting course, I don't have to sit around 6 of the ACA exams). If you are wanting to become an Accountant and to maximise your exemptions, check the ICAEW CPL site and search the course + uni to see what exemptions it can give you (and if there is a certain pass mark to achieve the exemption):
https://apps.icaew.com/cpldirectory?pk_vid=221c3da65a36f30f17178716467a95ffTaking the typical approach of studying Accounting (or Accounting and Finance like I did) *can* help with getting in if you mention it in interviews but the course you study isn't what they specifically look for. For graduate schemes, they hire based on your individual characteristics and quality: If you are teachable and willing to learn, motivated, align with their values, have reasons why you want to join them and the department etc. Only reason I mentioned STEM subjects was so that you may apply for grad schemes outside the scope of accounting (I've come across some non-accounting graduate schemes that want STEM degrees).
Going for PPE is perfectly acceptable to see yourself as a Chartered Accountant within 3 years post-graduating. If you want my opinion on a couple STEM alternatives, Mathematics for one and Economics for another. Both are respectable especially when studied at a Russell Group University. If I could do it all again, I would pick PPE at Uni of Oxford, due to how hard it apparently is and I would've enjoyed the Politics/Philosophy.