For what it's worth, I've now read about two thirds of Roud's book, and I don't recall having read any statements in the book suggesting that the vast majority of the English folk song repertoire of today originated in broadside ballads, written by professional or semi-professional broadside hacks. I could be wrong, but if he does say this definitively I don't remember it.

My overwhelming impression is that Roud's conclusions are overall of the "it's a bit of everything" type. I do recall Roud stating that claims of truly ancient antiquity for any given folk song are unlikely (and, more to the point, unprovable) but most of the time Roud seems to be pretty sanguine and philosophical about origins and proof. He is certainly sceptical about unequivocal claims to antiquity: for example, he challenges Bert Lloyd's unsupported claim that "we know" the Cutty Wren song to have been sung as part of a pagan winter ritual. But Roud is a very documentation-based researcher so he is just as scrupulous regarding any statements from the opposite end of the spectrum: as I said, I can't remember Roud endorsing any definitive statements regarding the polar opposite standpoint. Most of the time, it's a case of "there isn't proof of this" and, for Roud, what is sauce for the goose is also sauce for the gander.