Yes you can. Though if you have the grades to study medicine as a first degree I would highly suggest that route, as it is far easier to get in to compared to graduate entry medicine and the funding is much less complicated.
I'd seriously consider foundation programs and access courses before graduate entry medicine though.
Graduate entry medicine, as it is not a postgraduate degree, does receive funding. However, you still have to pay the first ~£3500 of year one yourself and are then funded thereafter. In addition, this is only confirmed for 2015 entry.The future for funding and the structure of the graduate entry route is a bit iffy though.
In all honesty I would only do a course you would be happy doing for the rest of your career as there is a significant chance you may not get on to a GEM course and to retrain after doing a first degree is a heavy financial burden if nothing else.