I would second that the Belgian system is very good. It is efficient, quick, and has a mix of private/public. When I fell and damaged my knee, I went to see the GP, who prescribed physio. I rang the physio (self employed), had my physio sessions for which I paid at the end, and reclaimed the cost.
Xrays/scans didn't just happen in hospitals. I went to what looked like a private house, but was in fact a clinic at the front, for a liver scan. Some GPs, in conjunction with a local hospital, funded a dedicated clinic where you could see cardiologists, dieticians, physios etc.
We need a reform of the NHS. There are other excellent systems out there. Co paying, as in Belgium, might be one of the ways to go.
PFI contracts need to be ended now. I think those companies have done very well from those contracts already.