Let me put this another way, Part II
In re: Britons travelling abroad for health care. UHC, or single payer, or whatever you want to call it, advocates are promising that we can have awesome health care at lower cost by switching to their model. No tradeoffs! Rationing is just a lie by conservative health care opponents who hate poor people! Look at Europe!
If this were actually true, the number of Europeans seeking health care abroad, other than cosmetic procedures, should be zero. If the health care is really every bit as good as what's available on the private market, they shouldn't turn to the private market. Americans seeking lower-cost health care abroad does not invalidate the market model; seeking lower cost alternatives through trade is a venerable free-market tradition. On the other hand, Europeans paying their own hard-earned cash in order to exit a system which allegedly provides exactly the same thing, for free, poses a problem for national health care advocates.