Europe is known for having single-payer, government provided healthcare. But just because there is significant government involvement in the financing of medical services does not mean that private hospitals are non-existent.
An interesting series of post by HealthcareEuropa looks at private hospitals that operate in Bulgaria, Turkey and Germany.
I think that the healthiest system is a balance between a strong public sector health service and top quality private hospitals.
In Poland, the public health system is inefficient, for specialized treatments and consultations to wait for months or years. So I opened a private clinic. The patient must be able to take care of your health, public sector, unfortunately, do not do this.