"Roll Your Leg Over" is distinguishable by

1. its virtually unchanging melody (clearly related to earlier ones),

2. the refrain "Roll your leg over, roll your leg over, / Roll your over the man in the moon."

3. randomly arranged verses (often numerous) of a more verbally ingenious, less traditional, more "urban-industrial" kind, suggesting a university or military origin. (The knife-in-the-window narrative has completely disappeared.)

The earliest ref. I can find to it is from the U.S. during WWII. Brand recorded it as the very first track of Volume I of "Bawdy Songs and Backroom Ballads," released in 1955. Not long after, he recorded more stanzas on Volume III.