I would ask around everyone that you can think of, the worst they can say is no. I think if you are looking for work in a university lab the best person to approach would be the head of the lab, the lab techs aren't likely to have much say, although they may have some good advice for you. I don't think experience in care work is hugely relevant, but at least you would be working in a hospital, you might make some useful contacts.
I think to get better info you could approach recruitment at the NHS and ask what exactly they are looking for, at least then you will have a definitive answer and you can plan your job hunt around that.