What a wonderful lot of research on one of my favorite Tim Hart/Maddy Prior songs! I just assumed that the buy-a-broom was a local product. Women who made brooms and sold them along their road are mentioned in Northumbrian song ("buy broom besoms"). But my assumption had been that most sellers of besoms (brooms) were *old* women, not "lish" at all.
Now I know about the Bavarian girls. That is clearly what prompted the song Hart and Prior sang, which first appeared in print circa 1860 -- maybe earlier, for all I know.