I would like to try out shooting with film.
Budget is probably less than £50 all in,
Hello and welcome. Despite all the debating that goes on here, we are all friends, really.
Film processing is (as you say) not going to give anyone with a chemistry background any kind of real problems. What you will do well to do is to read all about the process first and you'll find the usual stuff about dilution, keeping things spotlessly clean, temperatures even and consistent, and times accurate are all intrinsic in the film developing process. As you are in the UK (the reference to £50 is a dead give away), anyone able to get a GCSE in chemistry at high school, will know what is needed to make sense of it all.
NikoDoby, has said it exactly right about doing color ... don't do it first, its just that there is more to it is all and frankly its cheaper to send a C41 roll away to be done - at least that's what I found.
There are some outstanding bargains on eBay but by the time you add all the extras you'll find that fifty quid (about $75-ish US) is probably too low a budget if you are starting from scratch with film and find you really enjoy the old analog stuff. :-) You'll go through quite a few rolls of film and chemicals before you know if its really for you.
One tip I can give you is that as you are a student, get into using the facilities at your college. As a student, you'll usually get access to gear that you won't normally have access to. Once you graduate, if you do a part time or evening course you can often retain access to the darkroom and gear and teachers etc. Depending on the details, it can be a great bargain.
A good example; I work full time for a university and part of what I do is special event photography. While I have DX bodies and lenses of my own, at the uni, we have a collection of D3 bodies, accessories and lenses (some very battered and bruised HAHAHA), that I know I'd never be able to afford to use otherwise.
Anyway (from an ex-pat Londoner - I now live in the USA), good luck and enjoy.