Jim says 'Pity our knowledge of the oral tradition hardly goes back further than the beginning of the 20th century'. Absolutely.

However, many of these songs have a history that goes back well beyond that. A good number can easily be traced through a mixture of print and manuscript for 3 or 4 centuries. And in some of the versions (not all) it is quite obvious from the nature of the material that they have come from oral tradition at various points. Lots of examples if you want them.