I found this vintage book (no date), and even though it's in poor condition, I still thought it was cool. The Story Of Peter Rabbit, A Child Guidance Action Book. As you turn the pages, the figures move. Sort of along the lines of a Pop-Up, but they just shift, so there's some motion.
Mother Rabbit on her way to the bakery:
Peter, already in trouble with Mr. McGregor:
Jumping into the watering can to hide:
But Mr. McGregor heard him sneeze - Peter jumped through the window and ran home::
Flopsy, Mopsy and Cottontail enjoyed their supper, but Peter was too sick to eat (he must have hidden his head under the pillow!).
Still a cute book, even though it is messed up.