Not that this is super-reliable academically, but my mother [now almost 95] used to quote bits of this song at me. Her musical tastes would suggest she'd have been unaware of the Harry Belafonte 1959 version, and, unless Pete Seeger was a major musical force in England in 1949, nor his. [It's just possible my father, interested in folk song before it became widely fashionable, MAY have had a copy of the Seeger version, and she acquired knowledge of it that way, but there's not one in his collection as it now is]. What it DOES remind me of is the sort of material her father used to sing [light comic stuff] and he died in 1933. As I don't think he translated German, that hints at a well-enough known English one being in at least sheet-music form in the late 20s.
My favourite version is Flanders & Swann's "There's A Hole In My Budget", written originally about R A Butler and Winston Churchill, thus pre- 1955. For a successful parody, the original must be sufficiently entrenched in the public consciousness, which suggests a hit recording in about 1953 or before.