I thought I saw this thread a few months ago, and when I searched, there it was. I have a song from my childhood called Little Fat Policeman and I finally got around to recording it as an MP3. Here are the words:

Little Fat Policeman

Little fat policeman in the street,
Blows his silver whistle, tweet, tweet, tweet.
Some cars stop and some cars go,
When little fat policeman signals go.

Chorus:
Yo ho ho, yesiree,
Little fat policeman please save me.

Little fat policeman all alone,
In his little roundhouse with his telephone.
Ting, ling, ling, rings in his ear,
Little fat policeman 's always near.

Little fat policeman on the beach,
Keeps his feet dry and eats his peach.
Help, help, help, now don't fear,
Little fat policeman 's always near.