I just visited the "It's that Man Again" site, and listened to the brief bit on "Don't Forget the Diver" - I'm not at all sure it's what we're looking for, but I'm willing to bet that all the mine clearance divers in England in 1945 had heard that show, and some-one no doubt would have made a song.
These guys were all nutters, of course - they cleared beach obstacles before landings, were often in the harbours before surrender, working in the dark, in the slime, with incredibly crude rebreathers: no SCUBA then, and they couldn't make bubbles or they'd be dead) picture here Mine Clearance Diving Suit - 1945.
So I have absolutely no doubt that the bars in the messes were well populated, and that singing was a large part of the affair.
Just off the phone with my younger sister, who recalls Dad singing "Don't Forget the Diver, Forty Feet Below" to the opeing melody of "Lilli Marlene".