If there was a wait for the NHS - then the thing he wanted wasn't life threatening or urgent. If he then chose to spend money on private healthcare - that's his right and his choice. It doesn't say anything at all about the QUALITY of the NHS.
What DOES say something about it is that even a conservative as extreme as Thatcher refused to touch the NHS  - because it would be political suicide- it is just THAT popular.  Now the Tories have instead tried to drive privatization by gradually underfunding it - deliberately trying to make it not work well.
Deliberately vandalizing a service doesn't mean it didn't work well.

Now lets take another example. Canada. A few years ago Canada held a poll to select the greatest Canadian of all time. Names on the list varied from the country's founders to Wayne Gretsky and Celine Dion. The winner, by a landslide, was Tommy Thompson -the man who created their government healthcare system.
Canadians overwhelmingly deem him their greatest son of all time.