http://www.historyandpolicy.org/archive/policy-paper-08.html"The drive to make the NHS fully, or more fully, contributory was halted in 1962 by Enoch Powell's appointment as minister of health. To add to the irony, despite being an economic liberal, he also revelled in the launching of the alternative Hospital Plan, which he described as 'an opportunity to plan the hospital system on a scale which is not possible anywhere else certainly on this side of the Iron Curtain'. 'Command and control policy' came into its own as the focussed turned on how the money should be spent rather than raised."
Basically, the Labour party preferred the idea of funding from taxes (ie based on ability to pay) for ideological reasons; and the Conservatives who followed them didn't disagree enough to change it (and were already changing the pension system to one based on contributions, and didn't want to try to change the health system at the same time). The irony refered to above is
enormous; Powell is the most right wing cabinet minister that Britain has had since the Second World War - now mainly remembered for his racist views on immigration.
There is private sector health care in the UK as well; many (most, I think, but I can't be bothered to look up the figures) people use private dentistry, and opticians are private; some people also have private insurance, which provides doctors who can give you longer appointments, quicker treatments for non-urgent problems, guaranteed private rooms in hospital etc. Everyone uses the NHS for all urgent serious treatment. One advantage is that collecting the money is simple and inexpensive.