Where do you think funding for the NHS comes from? Taxes, which 99.9% of people pay.
Healthcare is free AT THE POINT OF CONSUMPTION, but it's certainly not "free". Therefore the UK is no different to the United States, the only difference being when it is paid for.
Of course you are right though I think proportionally we might still be paying less than the typical US citizen for their healthcare. Our advantage is that you don't pay more depending on the seriousness of your condition nor will you need medical insurance or be turned down due to an illness.
It mightn't be perfect but it's still better than most systems out there.
