Looking round & oval, it seems to have been The Times is generally considered to be the original quote, i.e
After trawling through library archives of newspapers, the earliest use of the quote I could find was in 1953. In London’s “The Times” I came across an article called “The Evolution of Football” [The Times, Friday, January 30, 1953; pg. 10] discussing the various forms of football, which goes on to say:
“….a large family – Association, Rugby Union, Rugby League, Gaelic football, American football, and Australian Rules. Each clearly has its merits and may safely be left to its adherents, but one cannot refrain from repeating the story of a certain Chancellor of Cambridge University (confessing complete ignorance of all football), who was asked to sum up a debate on Association and Rugby. “It is clear,” he said, “that one is a gentleman’s game played by hooligans; the other a hooligan’s game played by gentlemen.”
It would seem that this appearance of the quote in “The Times” was the source which popularised it around the rugby and soccer playing world.