The "working class" (particularly the urban working class) in the period when collectors like Sharp were active, were living in completely different ("Dickensian") circumstances to the mainly rural workers in earlier times. And many of those earlier workers were craftsmen, self employed people that nowadays, and even in victorian times, would have been regarded as "middle class". The "wage slave" was a product of the Industrial Revolution, possibly driven from the old way of life by the Enclosures. These events are well documented in folk-song.
Particularly as far as music is concerned the concept of these workers as unlearned is probably incorrect. I think it was Suibhne who mentioned this earlier, and just to back it up here are a couple of quotes;
from the Oxford Companion to Music referring to the Metrical Psalters (circa 1600);(Hymns and Hymn Tunes 5) "this was a period when sightsinging was a common accomplishment". And from Trevalyan's "English Social History", again referring to these psalters "these.... often supplied the music in four parts.... so that "the unskilful with small practice may attain to sing that part which is fittest for their voice". Which implies that
1. it was normal to be able to sing from music, and that
2. experienced singers would improvise appropriate parts on their own.
Again the first edition of The Beggar's Opera had melody but no bass. Well, a competent musician can play a suitable bass without the dots, can't he.
In any case, should we not expect a complete continuum of musical ability from the veriest amateur to the top professional; and so regard any division of this continuum as artificial.

GooseGander, I think you are coming from the wrong end about classical music. Yes, concert performances of beethoven will be very similar to each other, because the performers all play the same version, and indeed only that one version exists. The same applies at times to the "folk" scene today. But regarding folk not sounding like classical, apart from not sounding like Dylan (is Dylan folk?), Boyce doesn't sound anything like Birtwhistle either (thank goodness).
I think it was Beethoven who got cross about performers playing his music their own way (or was it Haydn), it was certainly normal up till then for this to happen.
Try a few (particularly newer) recordings of Vivaldi's "Four Seaons" and you will find they vary considerably.
And have you heard the renderings of Pachabel's Canon, as it is sometimes played in sessions?
But it's good to know what the composer intended, before making our own "adjustments".

Suibhne, my recollection of the classical scene is that knowledge of the teacher/pupil relationship is very important for tracing the handing down of technical matters and of interpretation, and regarded almost as a pedigree, so unlike the folk tradition the path of the classical tradition is well documented. (yes I know I said the distinction was artificial, I'm being an artificer)
For a modern example see http://www.violinist.com/blog/weekendvote/20088/8963/

And as you say the improvisation not only of music but of story was held in high regard. The old name for lyrics, the "lay", sounds very close to the "lie" told by "liars" or story-tellers.