It might be a little late, but try the Student's Union - or at least for the next academic year. I know that our SU (Kingston) had paid graphic design jobs for adverts and posters for the paper.
Try Craigslist perhaps? http://london.craigslist.org/
erm, and yeah, ask around for friends and family.
If there are any local businesses that have awful tacky leaflets, approach them and ask to re-do their image a bit for cheap?! Put flyers out and also diversify what you wish to do.
I've almost finished my degree and started getting experience and that in my second year. It is awesome that you're thinking about it now. I can't give you wise words of wisdom, but merely tell you how I tried to go abouts it.
Ideally, everyone wants to get paid, however, for most people/small businesses, it's also a risk to try a student and what not, hence working-for-free is often the easiest way. I spent my 2nd year summer shadowing a wedding photographer and eventually working for the SU as a photographer - though unpaid.
However, the purpose of relevant work experience is not solely to for the job experience itself, but also a way of meeting new people, and ultimately, networking. So don't discount work-for-free just yet (most of the time, they'll pay for your expenses or what not, so all isn't lost on a poor lowly student! LOL )
Some of my classmates have also gotten short jobs at developing websites and stuff, though how they did it is beyond me.
Hope it helps!