Hi, I am starting my access course this September & hope to study adult nursing next September. I volunteer at my local hospital & I think it's great experience. It can take a while to get everything in order (references/DBS check) so I'd start looking at the voluntary opportunities now.
St John Ambulance & Red Cross would be good too, like Deviant182 said.
You could always see if there are Bank Care Assistant Opportunies at Care Homes near you (they don't normally require experience) to gain experience in healthcare.
I'd recommend going to Open Days of the Universities you want to apply to, I found them a really good way to get more information about applying for the course & got lots of advice from academics & current students.
Hope this helps & Good Luck!