I am almost certain that doctors are paid by the government. For regular check ups we go to the doctors surgery for free, these kind of doctors are called GP's (general practitioners). This takes place in a building called a practice. Many of these are in Government buildings, something akin to a hospital, but without beds, or any type of operation more complex than in grown toenail removal or an X ray taking place. A group of doctors run their practice, often with a secretary. I dont know whether they pay rent to the government for the premises or just get it for free. But as healthcare for the patients is free, I assume doctors are either paid a flat rate for their work, or a fee for every appointment they serve.
I assume proper hospital doctors dont feel the need to set up these psuedo independent practices, the pretence of independence is probably pointless in this situation given how large hospitals are and the seriousness of the treatment.
Private operations are availiable in other clinics, but mainly for non essential work, ie. plastic surgery. For tens of 1000's pounds you could get a serous operation privately, thus avoiding the NHS's very long waiting times, but this is not affordable or good value for the vast majority of people. Another example would be people with a limited lifespan travelling abroad for an operation that the NHS sees as a waste of time and resources. 'You'll be dead soon anyway'.
Dentists do get paid government subsidies, but they are much less connected to the state health system, and increasingly many are abandoning welfare state work completely
Apologies if this is more info than you need or not properly answering the question.
