It was its egalitarianism that appealed so strongly to the population.
Perhaps there was also the hope that one would get more out of it than one had put into it, that it was a kind of lottery with a much higher chance of a winning ticket than in a normal NHS had no egalitarian effect, rather the opposite.
For example, in 2014 the Commonwealth Fund published a report comparing 11 Western health care systems.
According to the report, the British NHS was best on all measures except one, in which it was the worst apart from the US system.
The only perceived problem with it is that it is underfunded: the same problem as with all other government services.