Does the UK have the best health care institutions in the world?
Not in the present day time slice sense ("did he write "best," didn't he mean "worst"?"), but think of it over time. There is a big lock-in effect. The United States, for instance, cannot easily switch into another way of organizing its health care system. Obamacare is built upon current institutions and, for better or worse, does more to lock them in than to modify them.
Let's say you think an optimal mix is government-run clinics for the poor and reliance on the market for wealthier individuals, with people in the middle using some mix of the two. The government clinics enact redistribution at relatively low cost and this means you don't have to overly regulate the private market. People can take their chances with the market, or fall back on the cheaper but possibly inferior government service. Think of it as a public option at the level of provision rather than insurance.
Now that is not exactly the current regime in the United Kingdom. For one thing, the public sector is too large and the private alternatives are both too small and not free enough. But could you not imagine their institutions evolving into some version of this, mostly through growth of a less-regulated market sector?
Can you imagine the same evolution for the American system?
Addendum: Ezra discusses how the American system might evolve. And Austin Frakt comments.