Struggling to break in…

So firstly as a disclaimer, I work in IB, so I'm speaking from that perspective, but I think the "how to get in" is broadly similar.

Next, on course, PPE is totally fine. I asked my own firm's HR team about degree selection and they said they really don't rank one course over another - they have a lot more Finance / Economics / etc. in the groups they put through to interview than the general student population, but that's the result of a massive sample selection bias (+ my own speculation they might be better-positioned for the online numerical tests). So by extension at least at my firm (and we're not a niche boutique or anything), BA and BSc are viewed similarly, all else equal within reason.

Without knowing how senior you are (I'm going to assume first year), it's less about skills per se and more about your preparation and application skills. On how to prepare, I've posted the below elsewhere and editted it a bit for you, and hopefully relevant. 

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1) Be involved in finance / economics-related societies and attend their events, particularly career-related. I can't comment on specific societies without knowing where you're at, but all universities have the same sort of societies

2) Do a Spring Week if indeed your are a first year. Summer internship if second year / penultimate. Apply early and apply broadly. Get advice from people in societies. Don't faff about, get your CV sorted and send those applications out early rather than hesitate.

3) Get a role / leadership position in a society, or found one (probably more a Year 2 than Year 1 thing), but in your first year there'll be elections towards the end of the year so be aware of those, and there may even be roles for first years.

4) Network A LOT - try to find people who you have something in common with (same hometown, university, course, etc.) and be personal.

5) As far as technical preparations go maybe look at WSO or BIWS - I'm not as sure what you need or get tested on for S&T, etc., and these are not a formal course as such, but something to educate and prepare you for assessment centres, and indicate some interest in the sector.

6) Find some extra-curricular (ideally, relevant) activities for yor CV. Something finance-related is good, but absolutely don't shy away from having something interesting on there. A great way to grab you interviewer's attention is if you have something in common that's specific. Obviously you need to be lucky, but unless your hobbies are just plain weird or controversial, then listing your niche interests can't hurt (e.g. if you and your interviewer both have military experience, are both keen surfers, or both follow the same anime, it's a conversation-starter)

7) Some of the societies I mentioned above run investment or stock-pitching programs. It's been a while since I graduated so, honestly, I don't know how these work, but I see them increasingly on CVs and I'd imagine it's even more relevant in S&T.

8) You probably stand a good chance with IB / Consulting so do explore this too - appreciate not your indicated interest but it's good to have optionality so long as the cost of applying isn't high. 

9) Look into first year internships, or a volunteering program for your first year summer if you're a first year. Not a need-to-have but any additional relevant items for your CV are always helpful. These aren't especially common but I do increasingly see them (admittedly more on continental European or APAC CVs rather than British).

10) Hard one, but if you start your own business it's likely to show hustle. It doesn't need to be a successful business, but could be running a YouTube channel reviewing skateboards, buying a bunch of doorway pull-up bars and selling them on campus, or gutter cleaning or whatever) 

I probably forgot some things so hopefully others add. If you want some more advice about life (totally unsolicited) then do enjoy your time while at university, because it's your most valuable ressource and you lose it quickly. Find hobbies, travel, etc. Wish I'd picked up a martial art or learnt how to make a good cocktail or something. Good luck!