It may not affect how much a singer likes a song or how they perform it, but source singers often did know where their stuff came from. Look at the repertoire of the Stewarts of Blair as printed in the MacColl/Seeger book "Till Doomsday in the Afternoon" - Belle Stewart had a word (which I forget) for songs derived from the music hall and similar sources. She thought it was nice to know the difference between these pieces and those that had been circulating orally for centuries longer, as do I.

For a song from the other side of the Atlantic that we nailed an author for on Mudcat in the last couple of years, look for threads on the origin of "Oh Death".