Quality not Quantity - good quality experiences that teach you a lot will be far more valuable to you and your application than racking up loads of hours that you don't learn much from.
REFLECT! The key thing about work experience is how you reflect on the opportunities you take. When you go to work experience always ask yourself questions like: What did that teach me? What have I learnt from that experience? How has that experience helped develop me as a person? What transferrable skills have I learnt? How has that experience given me insight into the career of a doctor? Always ask yourself, so what? Why should the interviewers that are going to interview you care about that experience?
Ask your School - they may have established links with work experience placements that past students have done.
Ask your local Health Board - they will often have an Education Department. I, for example, did a week of shadowing in one of my local hospitals, which I organised through talking to my Health Board.
GP experiences are just as valuable as hospital experiences.
Being a carer is a good option too, and will give you some money through wages as well as giving you vaulable learning opportunities.
Do you know any doctors? If not, don't panic (I didn't either), but it is common that people get work experience by knowing doctors.
Be you and enjoy every opportunity. I am sure that if you get some work experience opportunities, if you attend and are enthusiastic and show your personality, you'll fit right in!