What relation do you think Investment Banking has to Maths OP? You seem to be sorely misinformed about industry aside from the long hours. Set aside any grand ideas about using your Combinatorics and Information Theory and instead, think M&A and raising capital (soft skills) and long nights (80 hr weeks) on Excel and PP formatting some text.
I know firsthand that Oxford has an excellent careers service, go and arrange a meeting with one of their advisors, but I implore you to do a basic Google search and read some job descriptions on Investopedia first. I’ll get you started, you can look up Private Equity, Risk, Financial Modelling, Quant Analyst, Hedge Funds, FX Trading, Asset and Fund/Portfolio Management, Wealth Management, Data Engineer (programming language such as Python), Commodity Trading, and a whole bunch of other trading jobs.
Not all jobs in finance have Investment Banking hours, do avoid Trading and PE if you do not like stress. Most Quants I meet nowadays have PhDs, since you actually have the skill set for it as an Oxford Maths grad, you should consider it. It’s not client-facing, the pay is very good, you can easily transfer offices (move to the States or wherever, Quants are always in demand), and you work normal hours. If you’re aiming for a grad scheme at any of the top firms in Industry like a BB bank and Fidelity and Lazard, you will need some experience such as a SA position and internship. Again, go speak to your careers service.