Bruce Olson and Murray Schoolbraid saw a clear connection, and that's good enough for me. Early examples are known from various British (mostly Scottish) sources, though it was re-made more than once by American commercial performers during the 20th century, presumably from American traditional forms. See DT entries

HILLI BALLU
HINKUMBOOBY

... and, in the forum (among others):

Lyr Req: here we go loopy loo
Obit: Larry La Prise (Hokey Pokey/Cokey)
and Hokey pokey and the Druids? (but only if you are bored)

Safest, as usual, to ignore some of the more extravagant suggestions in the various threads.