Your local hospital might take you as a volunteer if they won't take you for specific work experience. I just made cups of tea, cleaned and tidied and did patient satisfaction surveys. I say "just", it was invaluable work experience. I had open access all over the hospital and plenty of time to sit and chat to patients about their experiences. You are also a little invisible on the wards, so you really get a feel for how the team works (or doesn't work), the pressures and realities. Anything is work experience if you spin it right and reflect correctly on it. I recommend starting a notebook to jot down brief notes on what you did, a gut feeling and go back a week later to add another thought once you've had time to process it.
For example: In the care home you may be tidying up and you see a patient wailing in what you perceive to be pain. No one is paying any attention to her and you feel horrified. A week later, you realize the patient does this frequently, it's not pain, the patient is oblivious that they are doing it and everyone is really busy caring for other people because the home is tightly staffed. You make a note to research dementia and write three bullet points on how it affects patients and their families.
This way it'll be much easier when you come to do personal statement writing and interview prep.