Thanks Sandra. The origin of the song might not be Anon. More research needed? Interesting that the Greensleeves-playing Mr Whippy vans were also possibly way over in Western Australia.

The Twiliters - Creamsleeves

"The Twiliters was a 1960s folk trio from Perth, Western Australia. The members were Jim Maguire, Kerry White & Hans Stampfer.

"The studio version of Creamsleeves was a hit in 1965. On this live 1966 version the double bass is played by jazz great Ed Gaston.
Explanation for non Aussies: For decades one of the most ubiquitous sounds in an Australian summer was a tinkling rendition of Greensleeves emanating from Mr Whippy icecream vans which seemed to be able to traverse every street 5 times a day."