I've just remembered a handclap song from my own childhood. It goes like this:
Si si (or Cissy?) my platmate
come out and play with me
under the apple tree
for all the world to see.
Slide down the drainpipe
and through the cellar door
and we'll be happy friends
forever more, more, more more more.

I grew up & still live in Lincolnshire in England by the way as has my nanna all her life. We're both white british. She was born in 1929 & learnt the skipping song i previously posted as a child & I was born in 1980.