I've applied for psychology to start this September (I'm in year 13). It's not essential at all to have any kind of experience in a psychology-related field. Many psychology graduates go into market research, HR jobs, rather than straight up psychology/healthcare jobs. You need to demonstrate how you are suitable for the DEGREE COURSE, not a PSYCHOLOGIST.
Teachers told me my personal statement was quite strong for psychology so this is what I included:
I demonstrated my passion for cognitive & biological psychology, and mentioned a book I read. I then expanded my views on some of the points mentioned in the book.
I also talked about my extra reading of various cognitive research.
I mentioned my work in a charity shop and quite easily linked this is with the skills admission tutors look for.
I also mentioned quite a lot of my voluntary work/jobs and kept linking them in with what the admissions will want to see - communication, cooperation, working part of a team.
So I would recommend any kind of work experience you can get. You can easily link it in with a university application.