On a conventional Private Medical Insurance you may pay premiums for several years and if you do not make a claim you get nothing back. If you self fund then you have no guarantee that funds will be available when you need private treatment.
Medical savings plans have been developed in the USA and are now being introduced here. When these are purely savings plans they are a financial tool which this site does not cover. However, a new breed of part savings plans, part private medical insurance is developing. These allow individuals to build up their own health fund for paying medical bills. They also have insurance to limit how much the customer pays.