"I don't see how it could be argued with much credibility that such songs got to England via a purely oral non-literate tradition"
Over the centuries the motifs of our traditions were obviously carried by colonisers, traders, armies of occupation seamen, slaves and slavers, settlers all who needed to breach the language barrier in order to carry out their occupations to survive
Much of our repertoire stems from or was carried by the Travellers who probably originated in Asia and, having travelled The Globe, eventually settled in the areas they are still to be found - they are still recognised for not being literate

All of this existed in a world where literacy either didn't exist or had not become a part of the everyday life of the people who sang songs and ballads.
The motifs in 'Bruton Town' date back earlier than Boccaccio and those in Hind Horn as far back as Ancient Greece and Homer

One point that seems to have been downplayed by Roud is that our singing traditions were largely based around the home and not the streets and pubs.

Sorry for the interruption - I'll leave you to it
Jim