Good Wikipedia article on the various claims re origin and authorship {Jimmy Kennedy of Teddy Bears Picnic, Isle of Capri, Red Sails In The Sunset, Spreading Chestnut Tree &c a strong claimant; also bandleader Al Tabor, et al}, national variants in the name, & so on.

Seems to have originated in UK with some input from a Royal Canadian Air Force officer....   Maybe.............

https://en.wikipedia.org/wiki/Hokey_cokey

We used to go Looby Loo at Woodstock School in The Drive, Golders Green, London NW11, which I attended aged 5-7 [1937-39]: an in-&-out handholding circle for the chorus, breaking hold to perform the actions of the verses. Hokey not invented than, it would appear.

There was a doll character called Looby Loo in the children's tv programme Watch With Mother, mentioned above, 10 Oct 05, one of Andy Pandy's friends. Whether the dance/song featured also I am not sure.

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