If you work in city banking then of course you will have had to do a job specific degree at a university recognised by that sector. Thats no different to going in to medicine or law.
No, the point has been made by several people that many roles in the finance industry can go to trainees with mathematical/scientific/engineering degrees, not business and finance. I did a degree in nuclear physics before I became an accountant and, at the time I joined, the preference was for trainees who didn't have relevant degrees as they were less likely to start with preconceived ideas and had some experience of a different field - useful when auditing British Nuclear Fuels
The upshot is,
if you are going to do a degree, stick to the traditional maths/science/engineering degrees from one of the old universities rather than an ex-poly (Salford and Hatfield being exceptions
).
Personally, I would also advise modular training at the moment.
Cheers
Whirls