(Not a Historian, I studied politics and History in Britain in University. Sorry if this is a problem)

The whole reason many believe that Clement Attlee was elected Prime Minister in the 1945 election is because of the British public want for reform, of course their are many other reasons such as the lack of organization in the Conservative party's political action due to the truce and temporary pro-Soviet feelings preventing any red scare from happening and other issues people debate, but the fact that a post-war consensus emerged is pretty obvious. Something along the lines of an NHS was part of this consensus, The Beveridge Report was unbelievably popular among the people, some polls showed 88% of people who knew of it wanted its policies to be implemented. It citing disease as one of the five major evils in Britain at the time. The public had a genuine desire for change and they were willing to remove their beloved war hero Churchill from power to get it.

That's not to say people didn't argue about it, but the principle was very popular. Clement Attlee was also not for much debate and perfectly willing to force policies through using political intrigue and trickery if he must. When he decided Britain must have its own independent nuclear deterrent for example, he hid it's discussion in a secretive and innocuously titled "GEN 163" committee, from which he excluded Cripps and Dalton, economic ministers, because he knew they would object to the cost. He later hid £100 million from its proposed cost to get it passed. Britain had the bomb within 5 years of that committee.

When the actual details came into importance, Attlee appointed Nye Bevan as Minister in Health in charge of its creation. Nye was a fiery defender of the right of the public to free healthcare but was open to compromise when needed. He compromised with differing people who argued for a different solution to each problem and often it was the NHS that suffered for these compromises. The NHS ended up being ran by a board under ministerial control and divided into awkward localities with delegated power which were difficult to administer nationally and particularly difficult to set budgets for and set a semi-independent layer of bureaucracy between the minister and the NHS. This later impeded change and reforms later in it's history. David Reynolds called these problems a cancer in the heart of the NHS.

But largely, the NHS's creation as a principle was part of the post-War consensus and was agreed upon by a majority of people. If their were a large amount of debate, it would have been implemented anyway I beleive, Attlee would not have backed down on this issue.

Sources

The New Politics of the NHS: From Creation to Reinvention - Rudolf Klein

National Health Service: A Political History - Charles Webster

My education.

This is my first post of this type, I hope people are happy with it.

Edit: Fixed some spelling etc. Sorry, had to rush a bit but I tried to be thorough.