Yes, poetlady's got it really - it's the combination of willies AND cocks that does for that song. I can accept that Willy was not a double entendre until fairly recently - what about cocks though? I know that the, er, gendered use of the word comes from the "tap" sense, as in stopcock.

It's the premature cockcrow issue that makes me suspicious, in the context of the song. On the other hand, I've got it in the Penguin Book of English Folk Songs (eds R Vaughan-Williams and AL Lloyd), which suggests that R Vaughan-Williams and A L Lloyd didn't think it was meant as smutty. I guess... or that it was 1959 and they could get away with it by then.

Also, people probably shouldn't snigger, but they do, and I would rather not be the cause.