Martin Carthy records and sings it with the title The Bows of London - explanation here:

"The Bows of London
Ever since I head Jody Stecher sing a luminous song called The Wind and the Rain - a version of The Two Sisters - I have wanted to sing it. Its overwhelming feature is its concentration on that aspect of the story dealing with the building from the murder victim's remains of a fiddle which then takes on a life of its own and ultimately unmasks the murderer. Having found my own efforts at singing this to be as unconvincing as my efforts at American songs usually are, I cast around for a tune from this side of the water, came upon The Bows of London and then tried to stay close to Jody's words. A 'Bow' is the bend in a river."

The tune does fit the lyrics chillingly well.