The bulk of known material has never been published, and remains in various archives as manuscript notation and (more recently) sound recordings. The closest you will ever get to a 'master list' of known examples of traditional song is the Roud Folk Song Index; by definition it will never be complete, but it is the single most important and comprehensive catalogue ever compiled.

See http://library.efdss.org/

Note that the Index doesn't include arrangements of traditional songs recorded by revival performers (though you can often use it to find out where they got their material from if they didn't bother to acknowledge their sources) or, for that matter, 'art song' arrangements such as those of -for example- Butterworth, Vaughan Williams, or Britten; nor recordings of those.