Percy B. Green called this an "Essex Charm for a Churn, 1650 A.D." in his book "A History of Nursery Rhymes" (published in 1899).


Here's another version of this rhyme from Cole's Funny Picture Book No. 1, written and compiled by Edward William Cole (1st Published in 1879 in Melbourne, Australia):

Churn, Butter, Churn!

Churn, butter, churn! come, butter, come!
Peter stands at the gate,
Waiting for a butter cake;
Come, butter, come!