Helen wrote: To me the melody does not sound English or from the UK or Ireland but it does remind me of Jewish melodies.

A German text and a Jewish melody might suggest Yiddish origin. But I looked at the staff notation, and I don't think the tune is Jewish. Certainly not characteristically Jewish. You're just hearing the minor mode, I think. (Strict Aeolian minor, not Dorian or natural minor.) I suspect it's German.

I'm not good enough at German to date it, but even the German sounds fairly modern to me.

The description as an English folk song is clearly not true.