Helen - in case you were still wondering: the earliest appearance of this song in Germany that anyone seems to be able to find is in Gottfried Wolters' 1968 volume of his Ars Musica songbooks, published between '62 and '71, where it's just credited as being a 16th century English folk song along with a contemporary German translation by Hannes Kraft.
Sadly not much hope of tracking down its actual origins there.

Something that might not apply to this song at all but just feels worth mentioning is that growing up, a lot of songs originating in the third reich were rebranded and sold to us as folk songs from other countries... For example, "Über der weißen Nacht", a "Swedish folk song" we learnt in primary school, was never Swedish at all but written by (the horrid) Erich Scholz. Given both Wolters' and Kraft's history with the Nazi regime, it doesn't seem completely impossible that it became an "English folk song" because its original composer (/importer) had become unpublishable in the 60s?

That doesn't explain it being in English of course, or the number of people in YouTube comment sections that sang it at schools outside Germany.