That's a good point HR. If Churchill was anything, he was a political realist, a pragmatic politician. So when he got back into power after Atlee's government had created the NHS, by then he'd realised the NHS had broad support amongst the population of the UK, and be probably realised that to oppose it would be "political suicide".
It's ironic, sometimes a nominally "socialist" government can implement the reforms that Conservatives espouse better than the Conservatives. The best example of that in Australian political history was the decade of reform in the 1980s of the Hawke and then Keating governments.. ALP governments, Hawke was the former head of the Australian Council of Trades Unions... But his government's managed to get wage restraint, ( after a five year period of high wage growth and high inflation under Conservative government that was very hostile towards unions ) (0in exchange for introducing widespread industry based superannuation, and using tax reform and other policies to improve what he called the "social wage".. And at the same time pushed through reforms that improved productivity, floated our dollar, reduced tariff barriers, opened up our economy etc. His reforms set up Australia for a twenty plus year run of prosperity. It's a pity the decade of Conservative government that followed failed to match those reforms, and wasted a lot of the wealth on " welfare" for the middle class and wealthy and the Corporate sector, building in structural costs to government that are now causing real problems..such as over generous tax concessions for property investors and speculators that have largely caused an overinflated real estate price bubble.
The problem we have now is that the ALP are incompetent bunglers, and the Conservatives are hostage to the extreme right, hence the rise of independent MPs, the Greens, and right wing zealots such as One Nation