Just tried Googling it, and apparently it was on a Wonderloaf TV ad in the 1960s. I'm guessing Spurs fans adopted it for their Cyril. If it was in that old film, it must go back a long way.
Watched an old film today - "Belle Starr" with Gene Tierney, Randolph Scott, released in 1941. During the film some of the music was the tune to "Nice one Cyril" so it's been around for a while.
If Cyril Knowles was a left-back, how many goals was he expected to score? Maybe the line "let's have another one" meant let's have another hoof of the ball up the other end of the field.
The Cyril in the phrase is (or was - he died in 1991 at the age of 47) Cyril Knowles, left-back for Tottenham Hotspur football team (also known as Spurs) in the 1970s. However, the song existed before it became linked with Cyril Knowles. In 1972 the song featured in a TV commercial for Wonderloaf, which showed a jolly Nottingham baker called Cyril. After one particularly spectacular goal, Spurs fans starting chanting the song in honour of Cyril Knowles, and it stuck. The song even made it to number 14 in the hit parade in March 1973. It was sung by the one-hit wonders Cockerel Chorus. The full chorus is 'Nice one, Cyril. Nice one, son. Nice one, Cyril. Let's have another one!', 'one' being another goal.