What countries don't have socialized medicine?

No, There are few countries with socialized medicine. Britain is one.

Canada, on the other hand, does not have socialized medicine even though it has a single payer system. In "socialized medicine" physicians are direct government employees and hospitals are directly owned by the government. In Canada, for example, physicians are in private practice (except medical researchers & medical school professors) & hospitals are non profit with non government boards.

The only government involvement in Canada is paying the bills in the same way that an insurance company pays the bills in the US. There is no government involvement in decision making between patients and physicians, as opposed to the situation in the US where Medical Insurance Companies stand between patients & physicians, rationing care for profit & dictating treatment decisions to physicians.