On the contrary. If you were to scale up the UK’s NHS, America would save approximately $1T. Or, you could take the metric of percentage of GDP: America spends considerably more.
At least with the UK, you are reading the wrong sources. Don’t get me wrong: the NHS is far from perfect, but you mustn’t let the perfect get in the way of the good enough. And in the UK you can top up the NHS with private insurance.
According to UNICEF/WHO http://apps.who.int/iris/bitstream/10665/43184/1/9280638327.pdf here are the low weight births by country
Canada - 19/100,000
France - 51/100,000
Spain - 23/100,000
Sweden - 4/100,000
Switzerland - 4/100,000
United Kingdom - 52/100,000
United States - 323/100,000
Leave aside treating low weight babies, it appears that counties with universal health care have fewer low weight babies in the first place.
Among other things, because in those countries prenatal care involves a lot of zero-immediate-cost procedures which would cost half a kidney and a loan on your uterus in the US; delivery is again either zero-immediate-cost or a lot more affordable without needing to tilt against any insurance windmills. Obamacare has changed it, but none of my US medical insurances covered any “female conditions” other than abortions. It gave the impression than femaleness itself was considered not so much an illness as a horrible defect one should have avoided.
Submitting a payment request to my Swiss or Spanish private insurers brought no trouble, despite both being for care in another country (the Swiss one was the basic required health insurance, I’d hopped the border to a hospital in France because my French was less bad than my German; the Spanish one was travel insurance): the closest thing to trouble was the Spanish ones making sure that the low figures were indeed right (I needed to go through the process due to employer’s policies, otherwise I wouldn’t have bothered). In the US, every single submission involved several rounds of back and forth until the company admitted that well, ok, they really really really needed to reimburse me. I wonder, what is the cost of all those hours of back and forth?