Helen wrote: It has an unusual melody and rhythm and for me there is a similarity in the melody with the Autumn song, but maybe it's possible that the Summer song inspired the Autumn song.

I would consider this pretty unlikely. "Sumer Is Icumen In" is from MS. Harley 978, which is usually dated 1225-1250 though a few scholars date it 1300-1325. (Looking at the photos of that page kinda makes me think the people argue for the later date are right -- it looks more fourteenth than thirteenth century. No way that that hand comes from the sixteenth century, though.)

People call "Sumer" a "pop song," but there is no reason to think so; there is no record of it other than the Harley MS. Moreoever, it is the only poem in English in Harley 978. I think it's a one-off that was not widely known. The only real reason to think that it's non-classical is the rather earthy words.

Additional background can be found in its Ballad Index entry, http://balladindex.org/Ballads/FSWB260B.html.