There are several completely different traditional songs that sometimes have this title, though I didn't know that Dave Webber had added a modern song to the canon; as Dick Greenhaus has said more than once, titles are a snare and a delusion.  For example, in the DT:

CONSTANT LOVERS   (As I was a-walking down by the sea shore...)

The Constant Lovers  (A sailor courted a farmer's daughter...)

There are others.  Which one were you looking for?