This isn't really a song, really a piece of doggerel...everyone knows the first two lines, but it's my faint childhood recollection (some 40 years ago) that the original was from the Navy, has 3-4 verses and ends with
"and raise the flag WellDone"

This dates it, 'cuz the Navies haven't used flag signalling (with phrases particularly) in a long time.

Anyone have the full version? Google turns up plenty of hits of people's adapted first two lines, but not the whole thing.......