Here's one I learned at my mother's knee. Don't know if it's a children's rhyme or a grown-ups one. It probably dates from 1945 or so. Although I can sing it I can't remember the name of the original tune - it'll come to me soon!

Vote, vote, vote for Winston Churchill
Throw all the others in the dock.
Winston is our man, we'll have him if we can
And we'll throw all the others in the dock.
(By the cock!)