When mother says it's time for bed

by Lol
(England)

When mother says it's time for bed, up the stairs we climb.
We always took a story book, once upon a time.
Jack and Jill went up the wooden hill.
While Peter Piper played a lullaby.
Red Riding Hood was in the wood, Puss was in the well.
And while Bo-peep was counting sheep, Humpty-Dumpty fell.
So i think I'd better say goodnight.
Goodnight God bless, that's all I'll say, tomorrow is another day,
So I think I'd better say goodnight.

Who knows the second verse? Maybe it was an East end of London thing?