I assume that it was from Singing Together, There are a lot of the songs on the old folkinfo archive hosted on Joe Offer's site, but unfortunately 1962 is one of the gaps.

The booklet for 1962 is currently available on Amazon: BBC Broadcasts to Schools. Singing Together. Spring 1962, £14.90+£2.80pp (also listed on abebooks, very slightly more) if no-one comes up with the song. The contents aren't listed, but maybe you could ask the seller if the song is in it.

Mick