Yes, indeed it was Jake Thackray. And it's Yan Tan Tether Mether Pip - not pimp - although that does sound like the Welsh word for five.
I think a word of caution is needed when transcribing lyrics from Tony Capstick - I don't think he always got them right! I can only spot one Capstick substitution in the above though - it should be

Grow little sheep come wind come rain,
Fine warm wool for a lady's counterpane.