Trivia: The band "Toad the Wet Sprocket" took their name from a sketch on this show.
Trivia: The head of comedy at the BBC said that the title had to include the word "Circus", because the people at the BBC had referred to the six cast members wandering around the BBC offices as a circus, so added "Flying" to make it sound less like a real circus and more like something out of the first world war. And in front of that, added "Monty Python" because it sounded like a really bad theatrical agent, and also the large, constricting snake was also appropriate imagery.
Chosen answer: The song you talk of was originally a poem by William Blake called 'Jerusalem'. It speaks of the possibility of Jesus having visited England. The poem has four verses but you only ever hear the Monty Python boys sing the first one which goes, "And did those feet in ancient time/Walk upon England's mountains green/And was the holy Lamb of God/On England's pleasant pastures seen?" If there's any sort of in-joke connected to it's use, I'm not aware of it. It seemed to just be the standard song/hymn they used when a song was needed that wasn't sketch specific. Some of the sketches it appeared in were 'Salvation Fuzz/Church Police', 'Buying a Bed' and 'The Art Gallery Sketch'. Something that may be relevant, though, is that the only one who was present every time it was sung was Eric Idle. Perhaps he just liked it?