I'm not actually against a contributions based healthcare system, but the bar needs to be set really high and I mean those who earn over £100k per year. And even then I would have it on a sliding scale, so the more you earn, the bigger percentage you contribute. The way I see it, those on wages that are quadruple or more than the average can afford to contribute more to public services. I know some people will say, they pay higher taxes anyway, but it doesn't correlate to the actual costs of healthcare. I know it's a generalisation, but you'll find that the wealthy already pay into private medical insurance, so it's not an alien concept to them.
It doesn't sit easy with me, because I'm a staunch Bevanite that believes in the concept of free healthcare for all, but it's pretty clear that the NHS needs far bigger financial input to be effective going forward.
As for the US, their healthcare system is horrendously punitive. My friends in Ventura pay something like $1200 per month for basic healthcare and that only covers them for emergencies. Routine trips to the GP are extra and so is any ongoing treatment. They aren't wealthy. She's a baker and he's a radio editor, very much on the average American wage.
Although I can’t Claim to know too much about it, I think Germany has the right answer. A dedicated healthcare tax set at 8% of your salary, so the high end earners pay a bit more, combined with central government funding.