Those snips of articles that you posted indicate that the British health care system is underfunded and having problems due to budget cuts. The solution to that is simple: give the program proper funding. The problems they are having in Canada are the same.
If they had enough funding to hire enough medical personel, then there would be no waits for anything. The simple statistic to look at is number of doctors per capita. Regardless of the system (socialized or privatized), if there are higher numbers of doctors per capita, then waits will be less or non-existant. Same goes for other statistics like number of available hospital beds. If there are only a limited number, then there will be waits. If there are enough available, no waits.
It's simple logic.
Here are graphs comparing the US to a number of other countries in terms of doctors per capita & hospital beds per capita:
After looking at those graphs, it's easy to see why the French health care system is ranked #1 in the world.