I remember Kije and Cockatoo but not from Singing Together (although Kije clearly was on ST too). I think they both cropped up on a BBC TV series called Making Music. I think Petrushka (Stravinsky) was something else they adapted for that series

Ah here we go for Cockatoo from https://www.phyllis-tate.com/music-for-schools-and-young-people.html

In the mid-1960s BBC TV entered into the business of schools music. Several composers, including Phyllis Tate, were willingly pressed into service to compose pieces suitable for learning and performance by young amateurs. The originator and inspirer of this enterprise, John Hosier, recalls ‘visiting a little village school in Sussex of sixty children between five and eleven who had no other effective contact with music and seeing a lavish production that they had mounted of Phyllis Tate’s The Story of Lieutenant Cockatoo, which they had learned entirely through a sequence of eight  twenty-minute programmes on television’.

The Story of Lieutenant Cockatoo was a musical play, commissioned by the BBC as part of the 1968 ‘Making Music’ series for children aged 10-11. The excellent libretto by Ronald Eyre is a potted version of Samuel Taylor Coleridge’s lengthy poem 'The Rime of the Ancient Mariner'. The voices have singable, melodious lines, accompanied by chime bars and the tuned and untuned percussion usually found in a primary school, with additional optional instrumentation available for a Gala Performance.