Malcolm Douglas elucidated above, on 14 December 2002: The refrain, by the way, is one of many different ones and is probably of very little significance.

The Bows of London is Child #10 version O, and Child got it from Buchan: Ancient Ballads and Songs of the North of Scotland (1828) and Christie: Traditional Ballad Airs (1876). So you're right that the phrase is old.