I had thought that Golden Bough made up the tune for "Logs to Burn" and added it to the 1920 Punch lyrics, but I was wrong. Here's an e-mail I received today from Margie Butler of Golden Bough:

Dear Joe,

Thanks you so much for your email. I wish I could shed some light on the origin of "Logs To Burn". But, alas
I can't be of any help. I learned it many years ago, ( in the early '80's) from a folk singer on the West Coast named Linda Curry, who learned it from a singer from the East Coast.

I'm familiar with "the Woodcutters Song". I learned that version from Robin Williamson from Scotland. I'm sure both songs have the same origins, since the verses are exactly the same.

Good luck on your search.

Happy Holidays!
Margie

Katlaughing posted lyrics above that gives this attribution: Words Honor Goodhart, music Kevin Adams

Could it be that the Goodhart/Adams attribution is correct? The Punch lyrics pre-date the 1926 date given by Goodhart's grandson, so I think we need to keep looking.

Jack, I suppose one could say that "Woodcutter's Song" is an adaptation of "song of the Forest Trees," but I think that's a bit of a stretch. They're the same general idea, but have very little wording in common. It is clear, however, that "Woodcutter" and "Logs to Burn" are closely related because they share a lot of language.

In a 1966 issue of Country Fair Magazine (UK), there's a letter from Honor Goodhart:

I wrote the lines "Logs to Burn" in 1919 and they were published in "Punch." Some years ago the lines were quoted in "Country Life" as having been found in an old book belonging to the writer's grandmother. All this gives the lines a certain Ossian-like flavour.
Honor Goodhart, Newbury

So, maybe Honor Goodhart was the author....
-Joe-