The way they relate to traditional music is that in some way they are able to sit alongside traditional music in performance. In many cases they don't attempt to imitate traditional music, but they are capable of being performed in a similar way, which means that a folk club audience is more likely than not to enjoy them (not everyone of course, individual taste plays a part).

You insist on a homogeneity in folk clubs which, in my experience anyway, never existed. The clubs I attended always presented a broad spectrum of music, performed in different ways, but all broadly recognisable as "folk", and with a strong component of traditional music.

It is very difficult to pin down what qualifies a particular song in this way, it is often easier to recognise than describe, and there will often be room for disagreement. It may depend on whether the composer is recognised as a folk singer or is an outsider. I agree with you about Sheeran's song, not to my taste either. However the same could be said of a lot of contemporary folk standards, including some of McColl's output - "Dirty Old Town", for example, or "Joy of Living", both of which lack narrative structure, are strongly personal and written in the first person; none of these are characteristic of traditional song. Is that McColl's undoubted credentials as a folk singer make his songs more acceptable where Sheeran's are not?