Roy Bailey's record : "Why does it have to be me?" contains the following songs:

Welcome to the world
It's your birthday
Kangaroos like to hop
Irritating poem
Skin
Song of the clock
Free to roam
People
Rock a little baby
Questions
Why does it have to be me?
Vitamin dance
Nasty spider
Flying high, flying free
Everything possible

The record has been released on CD I think. A lot of the childrens' songs he sings are written by Leon Rosselson and can be found on various ones of his records/CDs. Leon Rosselson's songbook "Bringing the news from nowhere" is worth a perusal as it contains the music and chords, although it mainly contains non childrens' songs.

The best animal one is "Kangaroos like to hop", which has a simple tune and is easy to play.

Kangaroos like to hop
        And zebras like to run
        Horses like to trot
        But I like to lie in the sun.

        Hooters like to hoot,
        And bells like to ring,
        Scooters like to scoot,
        But I like to swing on a swing.

        Water likes to trickle,
        And milk likes to spill,
        Glue likes to stickle,
        But I like to roll down the hill.

        Creepers like to creep,
        And winkles like to wink,
        People like to peep,
        But I like to splash in the sink.

        Feet like to jump,
        And tummies like to hum,
        Knees like to bump,
        But I like to suck my thumb.

        Panthers like to pounce,
        And leopards like to leap,
        Bulls like to bounce,
        But I like to sing in my sleep.

        Kangaroos like to hop
        And zebras like to run
        Horses like to trot
        But I like to lie in the sun.

After singing hop, the children sing hop, hop, hop. Then run, run, run after run and ditto with trot. Same principle applie to the other verses.