In Canada we have basically the same system. I like it and i don't think it would go down well in Canada if anyone wanted to change it. In fact, they'd probably lose an election if they admitted they wanted to change it
People do complain about waiting times a lot though. Ive never really had to use hospital so i can comment much on that
But Canada has a higher life expectancy, lower infant mortality, more nurses per people and more doctors per people than UK so ha :P
but being serious, an NHS is pretty cool

America's system sucks