You can find broadside examples of the majority of "folk" songs. And in some cases the author is known. My Johnny was a Shoemaker, written 1859, is one example. The American composer, and his wife who was a singer, toured Europe in the 1860's, which is no doubt how the song came to be collected from the oral tradition. But did he base it on an older song? Who knows?

The folk song collectors just collected those that were remembered.
But no-one knows where the songs originated, and it is clear that the broadsides were often just existing songs written down (as shown by the numerous variants) and probably edited in many cases to provide a moral or a happy ending.

Nic Jones was one of the revival singers who used broadsides which he had discovered to great effect. But he did provide this information.