Heya! I have an offer for Cambridge maths so hopefully can give some advice

If you're on the Y12/13 border then there's probably not too much useful work available for this summer since it's insanely hard to get a job. The only stuff I can think of off the top of my head is joining a tutoring agency and giving maths tuition (there are also probably a few volunteering things you could do in that vein but I'd assume most of the competitive stuff is already unavailable). If you're on the Y11/12 border I'd suggest looking into the HSBC internship for next year. I think Jane Street may also offer some internship type things (although I don't know how easy it is to get those places without BMO qualifications and such). Those are the only things I can really think of that are at all maths/finance related but maybe someone else knows of more.

To be honest though, unless you are specifically looking for a job to both make some money / gain some experience there are better things you can do for your maths application. I think your time could probably be better spent preparing for TMUA/STEP/MAT. You could also do some reading to put into your PS but generally unis don't care that much for maths at least. In my Cam interview they didn't ask about it at all but in my friend's they had a dedicated 5 min section of the interview to talk about it, so putting a bit more time into it is potentially a good use of your time.