Spain Health system review
The series Health systems in transition by WHO is a helful source to understand the current state of healthcare. Now you can red the updated version for Spain. Check p.68 and you'll have to reduce the number of members with private insurance by 1.5m, because income protection products have been added,, and they don't reflect health insurance, they are "income insurance". Anyway, in p.61 you'll find the size of administrative costs, 3%. This is one of the reasons why the spanish health system is so cheap. But if you split between private and public you get the following: private insurance premiums are 10% approx of public expenditure, and represent half of administrative costs.I know that the estimation is quite difficult, but anyway, this is what the table says.
A big effort and a very helpful text for anyone interested in understanding the health system.