Doing work experience won't set you apart from other medicine applicants, everyone who applies has done at least a few weeks, and most will have arranged it themselves.
Basically, contact every hospital and GP in the area and ask for some relevant work experience. I reccomend that you actually phone them - they rarely reply to letters. Also, start some voluntary work (on top of work experience) ASAP. Spend a few hours every week helping at an old folk's home, or a special school or whatever. If you do all that, you're about equal with everyone else applying.
If you look around the medicine forum, there's loads of threads on this.