Hi Richard. I'm sure Ian can enlighten us more on this one. The spurious 'Edward' appeared over here somewhat miraculously in about 1770. If Sven I Rosengard predates that there can be little question about the direction of movement. Those few versions from genuine British tradition could easily be based on the literary Edward or even another translation in the 19th century.

Notoriously there are many examples of literary or redacted ballads being published and anthologised and then slipping quickly into oral tradition and quickly crossing language barriers.