I quickly found the same source for Tyne Exile's Lament. It appears to come from an 1888 "Beuk o' Newcassel Songs" compiled by Joseph Cawhill. It may be English, but it doesn't read like a folk song, the text is too flowery. And as Volgadon points out, it's set to a Scottish tune "Banks of the Dee" (although as I've pointed out elsewhere, it's found widely in the English tradition)

I don't know WAV's "Northumbrian Bagpipes" song but guess that it might be "The Northumberland Bagpipes" from the Roxburgh collection and printed in "Pills to Purge Melancholy".

http://www.traditionalmusic.co.uk/popular-music-olden-times-2/popular-music-of-olden-times2%20-%200536.htm

Again, it doesn't read like a folk song.

Of course, both are English but possibly not traditional, unless there is evidence that they have subsequently been collected