"Diddle diddle dumpling, my son John,
Went to bed with his TROUSERS on" is the version I heard as a child. (Just after the War)
Nursery rhymes were everywhere when I was small. 'Listen with Mother' on the radio, parents and grandparents, Infants' School, countless Nursery Rhyme books (Mother Goose, Kate Greenaway etc.) Children were expected to know the lot and to recite them when required. Most rhymes had a special tune to sing it to, and quite a few had actions or even a dance to do as well. (For example, Incy Wincy Spider, and Ring-a-Ring-O-Roses) My wooden cot had a transfer of Little Boy Blue in colour at the head, and Baa Baa Black Sheep at the foot. Even my little pink reins had a Mary Mary Quite Contrary picture on the front of the harness.