The radio programme used to get schoolchildren singing was called, appropriately enough, "Singing Together".
Jarvis Cocker did an "Archive on 4" about it in November last year. They even turned up some recordings!
I've just checked, and it's still available -
http://www.bbc.co.uk/programmes/b04stc6cI've been fascinated by the longevity of some playground rhymes. One we had in the early 1960s when I was at primary school went:
"Will you come to Abyssinia, will you come?
Will you come to Abyssinia, will you come?
Mussolini will be there,
Shooting bullets in the air,
Will you come to Abyssinia, will you come?"
This obviously refers to the war of 1935, and the rhyme had survived over a quarter of a century then, even failing to be "updated" when Nazi Germany became the aggressor.