Free national health insurance: Can doctors still be in private practice, outside the government system?

In England, Canada, etc., what happens if a doctor refuses to see government patients? Does he lose his license? Or are doctors forced to work for the national health system, as government employees? If a patient could afford to pay the fees of a private doctor, I'm wondering if there would be any in private practice and therefore whether the patient would have that choice. I would love to hear how these matters are handled in any country with nationalized medicine, and hear from patients, whether satisfied or dissatisfied. Also I'd like to know if a patient can still buy his own health insurance--that is, whether it's available. Or does nationalized medicine wipe out that part of the insurance industry? Thanks.
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I don't know about England or etc. but in Canada it is mandatory that all doctors work for the state. In fact it is a crime to have private health insurance or see a doctor outside the system. Currently the single largest group of criminals is the health care professionals. They know the true condition of a system that has an average wait of 16 to 18 weeks to see a specialist and maybe years of waiting for surgery. People in Canada with money routinely come to the US for heath care. That is anything beyond 2 aspirins. A friend in Seattle tells me you can't hope to see a doctor on Monday mornings unless you are willing to get in line behind a large group of Canadians. When I look at my family (extended) I believe that every one of them over 60 would be dead if we lived in Canada. My Mother-in-Law received open heart surgery in the US in less than 36 hours after seeing her primary physician. Mom would have died waiting to see a specialist in Canada. When she saw her primary her life expectancy was literally being measured in hours. I'm not yet 60 myself, just getting close, but I was diagnosed with diabetes a number of years ago. Under socialized medicine I would probably be dead too as I have developed a couple of infections that were potentially lethal and a wait to see a specialist would have probably seen the specialist coming to the funeral to check me out. I'm not a supporter of Socialized Medicine but I will bet the farm we are going to get it and if you are anywhere near 60 or if you have a serious illness I suggest you get your estate in order because the system will kill millions of older people. BTW, those are the same people who have worked their with the plan of taking care of themselsves. Now that idea is null and void and they will be expected to take care of 12 million illegals and those who won't care for themselves. EDIT: Did you know that Cuba has this system and when Castro got sick they brought in a Doctor from Spain. That should tell everyone something.
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