First recorded by Hal Kemp & His Orchestra feat. The Smoothies (US #2 1939).
Other hit version Kay Kyser (US #1 1939).
Also recorded by Frankie Howerd (1949).
From the wiki: “‘Three Little Fishies’ was written by Hal Kemp Orchestra saxophonist ‘Saxie’ Dowell, with lyrics by Josephine Carringer and Bernice Idins, and was first recorded in 1939 by Hal Kemp & His Orchestra with vocals by The Smoothies.The song tells the story of three fishes who defy their mother’s command of swimming only in a meadow pond, by swimming over a dam and on out to sea, where they encounter a shark, which the fish describe as a whale. They flee for their lives and return to the meadow pond in safety.
“The song was a US #2 hit in 1939 for Kemp but topped the Hit Parade when recorded by Kay Kyser, with vocals by Ginny Simms, Harry Babbitt, Sully Mason and Ish-Kabibble. ‘Three Little Fishies’ was released in the UK by British comedian Frankie Howerd, on the short-lived UK Harmony label, in 1949.”