Diggle2, I think you'll have to untangle a few different strands here:

First, about half of the responses will be from the UK and half from the US. This doesn't mean that the US responses won't be interesting, but they won't answer what you asked. The repertoire over there is very different - also, they sometimes take "song" to include "tune", which compounds the confusion.

I think that even within the UK you'll find there are big regional variations. Scotland has a different repertoire from south of the border, and I daresay its own regional variations. In England, the North-East in particular has its own distinctive songs, and other areas too will have their own favourites (East Anglia, Sussex, the West Country, etc).

Then, as you'll see, there are people who already have misinterpreted (or not read) what you wrote and are engaging in fascinating, if irrelevant, discussion on the crossovers between pop and folk ...

Anway, for what it's worth, here are a few songs that I think are in the category you mention, and that are widely sung and recognised at festivals etc in England:
Pleasant and Delightful
Come Write me Down
Adieu Sweet Lovely Nancy
Country Life (I like to rise..)
Raggle Taggle Gypsies (and its variants)
Various shanties: Leave Her Johnny, South Australia, etc
Banks of the Sweet Primroses
Seeds of Love
The Water is Wide
John Barleycorn
Byker Hill
Cadgwith Anthem
Rose of Allendale

Is that the sort of list you're looking for? I'd hesitate to rank them in any order or even to say these were any more popular and well established than another dozen or so songs that someone else might contribute. But maybe it's a start.
Marje