The songs in the English Country Songbook are by and large as they were collected from singers, words and music. A few of texts have been filled out with broadside words and a few have tunes assigned to them from other sources. (The appendix lists all sources texts and tunes, but as you say, on a song by song basis - mostly from the major collectors of late 19th and 20th centuries and recordings of source singers).

It a bit more trouble to get the sources in The Sound of History as they're not gathered together in one place - you have to look at the text near the song and the notes at the end. They are a mixture of songs that were collected with tunes and others that he assigned tunes to. (There are also some modern songs included with text and tune).

The songs in A Touch on the Times and The Ballads History of England were (IIRC) mostly from broadsides and as I said above Roy Palmer assigned suitable tunes to the texts.

Mick