Sorry for not responding earlier, but I've been stuck in elephant traffic on the Mumbei bypass since the Monsoon season opened and have only just made it back to the club for tiffin. I remember the song well, it was the night of the Regimental Dance, and Reggie hadn't turned up... so Eccles(the tall person in one boot) and his assistant Miss Minnie Bannister(she's not a true red-head you know.. .AEOUGH!)played that wonderful haunting ditty you describe so well..
It was non other than that old tyme melodie 'The Ying-Tong song'. I feel I must point out that in your drunken haze, the object you took to be a modern-type cardboard Kazzoo was in fact my batman's personal boot scraper, one 'Trooper' Bluebottle.

ying tong iddle-i-po