Have a look at this link:
https://www.cookdandbombd.co.uk/forums/index.php/topic,8769.30.html
Go through the two pages on the link and open some of the links on them. The song was sung by cartoon-like characters during an intro inserted deliberately or accidentally in a "Within These Walls" episode. It was featured on a "It'll be alright on the night" episode and you can watch it on Youtube via one of the links.
I don't remember it but it seems kids in school playgrounds everywhere were singing it the following day! Just maybe that's why you remember it so clearly.