How can I go about looking for work experience within the NHS?

I’m an undergraduate in the UK looking to start a career in healthcare, although I’m not sure what aspect yet. I’ve undertaken some work experience with Paramedics but would like to also shadow nurses in various departments in a hospital. I would love any advise on how to go about getting my foot in the door with this as I’ve tried emailing and calling local hospitals but I don’t seem to be getting anywhere with that; I also feel like I’m hassling busy people! I’ve set up a linked in and am currently trying that out to see if any insiders can lend a hand. Other options welcome! Thanks!