"Man in the Woods" is a German. folk song. It was QUOTED by Mr. Humperdink, a German composer, in the opening scene of Act Two Hansel and Gretle (1893).

In a British 1955 songbook for elementary (6 year old) the illustration is of a plant commonly known as a Jack in the Pulpit. I do NOT believe it is about mushrooms.

Sincerely,
Gargoyle

I attended a British School for awhile.