It even continues today.
The Brits and Canadians have some legitimate, sincere grievances with their systems. Systems that are increasingly dysfunctional in no small part because conservative and neoliberal governments continue to cut deeply from them, removing the necessary personnel and funding needed to let them do their jobs.
Increasingly, these internal politics around Canada's federal national health insurance or the British NHS are used as arguments for why we shouldn't make a change in the US, though. Which is like saying you should keep living in a tent by the river because the affordable housing in the next town over has some leaky plumbing.