How about "The Worst Band in The World"?

https://www.youtube.com/watch?v=-sraKulMHZw

Actually, one of the better bands at the time even although they weren't folkies....

From around the same time

https://www.youtube.com/watch?v=tb63PdPweDc

Strong contenders for both the worst band and worst song although I was singing it at The Royal Highland Show last week. ;-))