A health care system can be 2 out of 3 things: High quality, widely accessible, low cost.
Britain has chosen low cost and accessible thereby sacrificing high quality. As a point of pride, Brits love to point out their system is "free" to all making it "accessible." Though the lengthy waiting lists across the country to see a physician or get a procedure make accessibility debatable. If food were a human right and "free," imagine the crappy quality and long lines.
America has chosen high quality and accessible, thereby sacrificing low cost. High quality is obvious - best doctors, hospitals, cancer survival rates post diagnosis, etc. Accessible because anyone can present at an ER and get treatment without being asked about ability to pay (foreigners don't understand this). Medicaid covers the 70 million poorest Americans. Because we've chosen the first two things, America's system is definitely not low cost. We have the highest per capita spend by far, and arguably middling health outcomes and life expectancy. But those latter things are due to factors beyond doctors and hospitals. Our urban violence and general underclass challenges drag down our averages. You could put the Mayo Clinic in Port-au-Prince and it wouldn't make a huge difference.