There is nothing to prevent a later author from placing copyright on his version.
The musical scores in the book 'SONG SESSION' are copyright as of the date of publication (or specific dates for songs whose scores are copied in the book).

The song may be descended from "an old British song," but later versions are eligible for copyright. Certainly the song as sung by Rudy Vallee and others in the 1930s varies from previous related works, and is copyright. Others also may be copyright if they differ, partly or wholly, in lyrics and/or melody.