We have what you yanks call "socialised medicine". Everybody can get care "on the NHS" - the national health service, which the government pays for completely and which is free to access as the point of service.
But if you have enough money or a good enough job, you can get private health insurance to go see private (i.e., non-NHS) doctors. They're generally considered to be MUCH better, if only because the good doctors leave the NHS because they can make so much more money and have better working conditions in private practice. But also, they get paid to make you happy -- because you're the person bringing their money, not the government -- and they'll run any tests or do any treatment that you can afford if it's relevant and ethical. NHS doctors tend to "ration" care because of budgetary constraints.