This is what I learnt through the process of getting work experience...
Getting work experience takes a mix of luck and persistence. I was quite lucky with work experience, I was given the name and email of a specific doctor in a hospital and he organised my work experience for me (after I was told by someone else that there was no more places for work experience in the hospital). I didn't even know this person. But my work experience was organised in weeks, for some people it can take months and months. For a friend, they kept emailing and they also got work experience (but it took longer for them to organize), just be patient, keep persisting.
Utilize any "contacts" you may or may not have. Tell people you want to do medicine and that you are looking for experience. I met one of my sisters friends parents, I had a chat with them and said I was applying for medicine. Turns out they were both doctors (one in a hospital and the other with their own GP practice) and they offered me work experience. If you know a doctor or you know someone who works in a hospital (or someone who knows someone) then ask around and see if someone will help you.
When you get work experience, if you are friendly and positive someone else might offer you work experience or give you some useful information. For example, while working in the GP surgery I was offered, by a district nurse, a day with her in the community. Also, when I was at the hospital a nurse had a coffee with me on her lunch break and talked to me about working in the hospital and dealing with patients.
Once you get work experience make sure you get as much out of it as possible. Also, be willing to do menial tasks as well as. After each day I would take some notes of things you did and things you learnt and any anecdotes etc. as these will be useful when you are preparing for interviews and can't remember much from your work experience.