OK then, Mr.Happy, to get slightly more erudite and learned about this: the second half of the melody for each verse on the Kididdles version that I posted above seems to use a tune similar to "The Farmer's In His Den", which is not usual in Great Britain. The version of the song as sung and danced by Looby Loo on "Andy Pandy" simply repeats the first half of the Kididdles melody over again, where Looby Loo sings:

You put your *right arm* in,
Put your right arm out,
Shake it a little, a little
And turn yourself about.

(*etc. with various body parts of your choice)

Andy Pandy can do it quite well, but Teddy always gets into a terrible muddle and is told off by the disembodied lady announcer from Surrey with the frightfully nice speaking voice.

Other Andy Pandy songs worth researching are:

Andy goes riding, carefully, carefully,
Ting-a-ling ting-a-ling ting-a-ling ting. (x2)

Also:
"What's in the box ? What's in the box ?
Andy is trying to undo the locks" (the Escapology episode).

Oh, and then there's:
"Marching, marching, marching up and down,
Marching, marching all around the town."

Bye bye, everyone, bye bye

- jeanie (scarred for life from watching 1950s children's TV !)
P.S. Sarah and Hoppity lyrics can be supplied on request, and Torchy the Battery Boy.