I hesitate to intervene and resurrect this thread but as an early modern historian interested in the distribution of language and ideas can I suggest some of the following academic works which are very relevant to the issue of whether broadside ballads were the origin of (many) folk songs.
Fox, A., Oral and literate culture in England, 1500-1700 OUP, Oxford, 2000 investigates the relationship between oral and literate culture with a modern evidence based approach including Chevy Chase and Robin Hood.
Fox and other writers refer to Thomson, R. S., 'The Development of the Broadside Ballad Trade and its Influence upon the Transmission of English Folksongs' (unpublished Ph.D. dissertation, University of Cambridge, 1974) . traced 80% of folk songs collected by early C20 collectors to printed broadsides, inc over 90 which could only be derived from those printed before 1700. Suggested the great preponderance of surviving ballads can be traced to 1550-1600 by internal evidence. I have not found anyone who has taken this work further, or questioned it. I went to the UL to read this and my notes include the following:
p.2         complements book by G. Malcolm Laws, Jr., American Balladry from British Broadsides
p.15        Notes origins of some folk tunes in C10 and C11 liturgical tunes.
p.28-9 They did circulate in MS and there was a 'ballet' seller in Oxford in the 1520s selling >20 a day and a Proclamation was issued in 1533 against 'fond books, ballads, rimes and other lewd treatises in the English tongue"
p.125        "sizeable proportion" of works in Percy's Reliques derive from broadsides printed by Dicey and collected by Percy. 69 can be shown to originate with broadsides in the Pepys, Roxburgh or Percy collections.
p.171        Chettle in Kind Harts Dream 1593 says those joining the ballad selling trade included "idle youths, loathing honest labour and despising lawful trades" to be found in every corner of the kingdom "singing and selling of ballads and pamphlets full of ribaudrie and all scurrilous vanity. That stationers would put out their apprentices of a few months standing with "a dossen groates worth of ballads" and if they were successful and trustworthy promote them to be chapmen.
p.180        There exists a printed itinerary for ballad sellers dated 1625
p.216        Relates visits to Harry Cox of Norfolk over nine years to 1971.C ox had first been collected from by E J Moeran in 1921. "It was immediately clear that Mr Cox had a sophisticated awareness of what a folksong was as distinct from a music hall item or a popular song. In addition it was apparent that these distinctions had evolved during the process of meeting collectors, in other words information had been both given and received." Although many songs identifiable with ballads he claimed never to have learned them from sheets, although his mother bought them, but from others singing a song 3 or 4 times. When asked he had a large collection but claimed he learned the melody that way, and the words from manuscripts notes on miscellaneous papers over 7 or 10 days.
Thompson also notes that in USA, where there is no stigma in using paper sources, families produce such collections as heirlooms.
p.273-4        Collection of Alfred Williams in upper Thames Valley 1914-1916 included 755 texts of which 265 published in Folk-Songs of the Upper Thames, 1923. Williams noted sources from ballads. >600 can be traced to ballads printed in the region in C18 and C19, i.e., >80% and "the same figure (if not a little higher) is true of the collections made by Cecil Sharp, Vaughan Williams and Percy Grainger".

As to how these were distributed I thoroughly recommend "Small Books and Pleasant Histories ; Popular Fiction and its Readership in seventeenth Century England" by Margaret Spufford (Methuen 1981). My notes from that include:
p.viii         Notes in 1553 a man offering a scurrilous ballads "maistres mass" at an alehouse in Orwell, and a pedlar selling "lytle books" to people, including a patcher of old clothes, in the outlying village of Balsham in 1578. Both near Ely.
p.2         One publisher of chapbooks had in stock one book for every 15 families in the country
p.11         Richard Johnson's Seven Champions of Christendom , 1596, believed influential,(e.g. "In comes I, St George"). Evidence that at least 3 separate local plays include elements taken from printed work; a ballad grafted onto the Swinderby Play; passages from Diphilo and Granida, a pastoral droll by Cox, in a Somerset play, and dialogue from Wily Beguiled, in the Broughton Play. (all from C R Baskerville, The Elizabethan Jig, Chicago, nd).
p.14                In 1520's Oxford bookseller, John Dorne noted in his day-book selling up to 190 ballads a day @ a halfpenny each.(F Madan, ed. 'The Daily Ledger of John Dorne, 1520', in Fletcher C R L, ed., Oxford Historical Society, Collectanea, I, V, Oxford 71-177, and separately 1885.)
p.48                prices of chapbooks 2d. to 6d., when agricultural labourers wages 12d. per day.
p.49                contemporary reference to use for toilet paper, ("Bum Fodder"), for wrapping or baking.
p.98                Inventory of the stock of Charles Tias, of The sign of the Three Bibles on London Bridge, on his death in 1664 included books and printed sheets to make 37,500 ballad sheets. Tias was not regarded as an outstanding figure in the trade.