The system requires numerous feedback loops and clinical overview (ours is called NICE - National Institute of Clinical Excellence).
Is it perfect, no, few human things are.
Is it massively preferable to the average healthcare situation for Americans - hell yes it is.
I pay for my prescriptions which is £9 per drug per month (whatever the cost to the NHS of that drug is), I take 3 drugs so that should be £27 per month except they considered that case and I buy a NHS Pre-Payment Card which costs me about £10 a month and covers me for any number of medications. [1]
So for £10 a month I get the routine medications I need to make my life not just bearable but enjoyable which allows me to work.
So if costs controls in government are your concern the elect better people with better systems.
Lest anyone think I'm all sunshine and roses on the NHS, it requires drastic reformation (and they really really need to get rid of their 'internal market' way of running) but the idea is as sound now as it was in 51 years ago (almost to the day, it was founded July 5th 1948).