Well, just for clarification, since we're now into an in-depth study of ice cream, whimsical songs, and silly dances, which was my fault in the first place.......
The inspiration for the wartime participation song (with built-in dance steps), might or might not have been the "Hokey Pokey" flavour of ice cream. But even if it was, the song's title (and by extension the dance's title) was soon changed to "Hokey Cokey" - again for a possible variety of reasons. I can state with near certainty that the song and dance movements are both nowadays solely referred to in the UK as the "Hokey Cokey", as I believe has been the case since at least one generation removed from mine. Not that we all DO the "Hokey Cokey" on a regular basis, you understand.......