Think this list sums it up a lot (I remember ALL of them)!
Nellie the elephant - Miller, Mandy
Runaway train - Delhart, Vernon
Middle of the house - Cogan, Alma
Grandfather's clock - Radio Revellers
Owl and the pussycat - Hayes, Elton
Puffin' Billy - Melody Light Orchestra
All things bright and beautiful - Uncle Mac
Robin Hood - James, Dick
How much is that doggie - Pinky & Perky
I've lost my mummy - Harris, Rolf
Laughing policeman - Penrose, Charles
My boomerang won't come back - Drake, Charlie
You're a pink toothbrush - Bygraves, Max
I taut I taw a puddy cat - Blanc, Mel
Teddy bear's picnic - Hall, Henry
Ballad of Davy Crockett - Ford, 'Tennessee' Ernie
Hippopotamus song - Flanders & Swann
Jake the peg - Harris, Rolf
Gilly gilly ossenfeffer katzen... - Bygraves, Max
Woody woodpecker - Blanc, Mel
Who's afraid of the big bad wolf - Pinky & Perky
Ugly duckling - Cribbins, Bernard
I know an old lady - Pertwee, Jon
Bee song - Askey, Arthur
When I see an elepahnt fly - Peterson, Clive