There is very little that you will be able to do, due to problems with confidentiality and such. Most places will only give work experience to people who are already doing a degree/who have finished.
Most students will not have work experience. However, one idea which I thought of (but never got around to doing) was to contact a local mental health organisation such as MIND. You could volunteer as a befriender. Anything which involves working with a range of people could be helpful.