Several things people seem to not have mentioned, firstly we have smaller tax% and we tax lots of things, because it makes people feel better than having their wage being they only thing taxed, having it taxed directly at 60% and everyone feeling that working is pointless and not for themselves.
Secondly, the uk has far less industry, manufacturing and in general, real jobs than the USA. A HUGE amount of our ever increasing tax spending is going on new completely unneeded jobs in public sectors that are created to essentially do three things, hide the unemployment numbers, and hide how bad the economy is and keep the economy house of cards going by constantly recirculating the same money, money is earned, taxed, given to extra public workers, which is then taxed, and spent again and again in an ever increasing loop.
Without the extra jobs, we'd have several million more unemployed people that we currently have all needing handouts to afford things like food and shelter and we'd be being taxed directly for helping those people, this simply looks better for the government.
Neither can you really compare the situations in the USA or Japan, Japan has a heavily heavily concentrated population on a tiny landmass, so you save money by having one bigger hospital cover the same amount of people that two hopsitals in the Uk would need over a much larger area, each needing to offer basic services with a large catchment area with relatively few people in, in other words theres a HUGE amount of waste due to the lack of concentration.
Almost the opposite is true of America, but being that the place is huge, they have far more GDP and population they swing the other way, they can buy supplies for building roads in bigger bulk for better prices, they have a huge country with not infinate, but plentiful cheap natural resources while the UK ships in so much stuff it needs. America is a manufacturing powerhouse while the UK doesn't create any of the stuff it uses, be it in the NHS or anywhere else. For instance say syringes, maybe we import them from japan and they make the profit, while america's so big they have a company there that makes them, sells them cheap to the USA and makes profit selling them to other countries.
We're somewhat caught in the middle, also bear in mind that purely because the NHS is free, we get FAR to many people that go in just for a cold and beg for antibiotics, which are subsidised by our government. While in America you'll get lots of people both rich and poor as even rich people with good private insurance as with any insurance, premiums increase the more claims you make, when they have a cold due to the costs involved they'll stick it out so hugely less waste.
A different but same end result occurs in Japan, they aren't all fat unhealthy slobs, they have a far healthier population by and large who eat better and have less problems with their health throughout life. That means, less colds, less heart disease, less this that and the other, which means a hugely smaller burden on their health services, less people going on, meaning less demand at any one time, less wastage etc, etc.
The very nature of our "free" NHS puts it under more pressure than anywhere else in the world. This is why a free NHS actually isn't very good, when somethings free people use it without a seconds thought and waste lots and lots of time and money in doing so. If they added even a slight fee, like a £50 charge for every initial GP's visit, a Huge number of people with simply colds will wait an extra 2 days rather than pay and find they are better. Considering people with colds is the biggest load on local GP's ,it would save the country millions, and millions and millions.