Aaaaa, you Brits just like to take credit for everything...

I had most often heard it attributed to R. Service and it seems to me well in keeping with his style, but anything that obscene is probably not going to have the author or authors leaping up and saying "Me! Me! I wrote it, yes I did."
And as others have said, it certainly could be a parody in the style of Service.

But apart from the obscenity factor, I fail to see how the humor (or humour) in Eskimo Nell is that different from say, the Cremation of Sam McGee.
Blessings
Barbara