Well, we can begin with the above mentioned riddle song. It exists ina 15th century manuscript, and was still sung in oral tradition in the 20th century. Any others?

Summer is a cumin in is of course an old song, but didn't survive in oral tradition to be collected, so

1) we can't be sure it was a "folk" song

and

2) we can't be sure if it was ever sung between being written down and being set to music by some clever modern person.

So I'm not sure it fits what Tansy was asking about.