As the BBC noted (with my emphases),
The National Health Service (NHS) was established [on the 5th of July 1948] as a result of the 1944 White Paper, A National Health Service.Niall Dickson, Chief Executive of the King's Fund, said that, despite all of the other changes,
It set out the two guiding principles. Firstly, that such a service should be comprehensive, with all citizens receiving all the advice, treatment and care they needed, combined with the best medical and other facilities available. Secondly, that the service should be free to the public at the point of use.
one principle has remained: that the NHS should be funded from general taxation and available to all free at the point of use.(Geoffrey Rivett's written a good short history of the NHS.)
With conditions and caveats, we are already paying for prescriptions and optical, dental and orthodontic treatment and some unfortunates having to pay to access expensive medicines or treatment faster than they would on the waiting list (and here I mean those who can't afford to wait, rather than those who can afford not to wait).
I don't know if this is old news back in Britain, but I just saw that in the Financial Times on the 19th of March 2007, Nicholas Timmins reported that the "NHS may be restricted to core services":
The National Health Service might provide only core services, with patients forced to pay for any other treatment or meet it from private insurance, the government has revealed on Monday....Am I being too pessimistic to think that we're not going to get some model of a social insurance scheme and that this privatisation or otherwise dismantling of the NHS is just going to disenfranchise some people, to let some people fall through the cracks? Isn't the dismantling of social welfare truly anti-social behaviour?
The health department confirmed it was "looking at the possibility in the normal process of policy development" and agreed that deciding what everyone was entitled to would also involve deciding "what they are not entitled to"....
Anna Dixon, deputy director of policy at the King's Fund think-tank, and a specialist on international health systems, said: "It sounds like establishing a core package of benefits that the NHS will fund - and that is something that has long been debated in academic circles. But politicians... have always shied away from being more explicit about entitlements."
Social insurance systems tended to be much more explicit about what was and was not covered, with private insurance markets developing to cover excluded treatments, she said.