Songs with Hand Motions

My husband (who is English) sings this little song to our son:

   Round and round the garden
   like a teddy bear
   One step, two step
   tickle him under there (underarms)

London Bridge is a great song for kids.

Also, do you know This Old Man, he played one (etc etc)

Does anyone know the words to the Little Bunny Foo Foo song?  I only know the first verse (Little bunny foo foo, hopping through the forest, picking up the field mice and bopping them on the head)  Perhaps not a nice song for a young child!

I just remembered This Little Piggy Went to Market - toes not hands though

Five current Buns from the Bakers' Shop. 
Round and fat with a cherry on the top
Along came xxxx with a penny one day
Bought a current bun and took it right away.