Belatedly realised I should check the sleeve-notes to 'A Song For Every Season' - not a lot of extra info, but it indicates that the Coppers picked the song up from 'Bing' Dudeney; this is the only song in the 4LP set that they passed on, but perhaps there are others in the full family song-book?

Song title: Thousands or More
Name of performer: Bob, Ron & John
The Copper's source for the song: 'Bing' Dudeney
The title of the song given in Margaret Dean-Smith's Folk Song Collections 1822-1952: Not in guide
Bibliographic reference: CBL* (*'sets in this booklet', ie no external reference)
Broadside reference: No broadside version