Monkey Hips & Rice--The Five Royales (1953)
The Five Royales are the group that gave us Laundromat Blues (1953), one of the few songs out there on the subject of washing machines.
And I bet the censors listened to that "Laundromat Blues" a time or two back then! (Don't even mention her "spin cycle"!)
The closest I can come to a washing machine song is "Leader Of The Laundromat" by The Detergents, or the very distant cousins, "A Washer Woman's Blues", by Bessie Smith, and "Irish Washerwoman" by Pa's Fiddle Band.
Now, to get back on track for this thread -- the theme of the Harlem Globetrotters, "Sweet Georgia Brown" by Brother Bones.