Hello Mike,
I think I know the source of Ray Driscoll's "Death of Queen Jane".

It may have come from "John Jacob Niles - Sings American Folk Songs" (1956). Take a listen here:
https://youtu.be/biI88z2HzU4

Ray's version was recorded by Gwilym Davies in 1993. The Ray Driscoll CD booklet notes say he learned the song from an itinerant farmworker in Shropshire called Harry Civil, who used to work on a nearby farm and sleep in the barn.

My best explanation is that Harry Civil heard the Niles recording somewhere, or learned the song from someone who did. The words and tune are so close that it can't be a coincidence I think.

I'm sorry for drifting off here, but there's another interesting example of an American song being collected from an English singer who learned it directly or indirectly from a record.

The Devil's Nine Questions (Child 1). Jeff Wesley sang it under the title "Ninety-Nine and Ninety" to John Howson at Whittlebury, Northamptonshire, in 1988. And he had one stanza that went:

A babe's more innocent than a lamb
    Sing ninety-nine and ninety
And she-devil is meaner than womankind.
    And I am the weaver's bonny.

The song originally came from folklorist Miss Alfreda Marion Peel (1890–1953) of Salem, Roanoke County, Virginia, USA. She collected it from a Mrs. Rill Martin of Mechanicsburg, Bland County, Virginia, formerly of Giles County, on September 11, 1922.

And Mrs. Martin sang "The Devil" in that verse. She-Devil, amusing as it is, goes back to a misreading of Miss Peel's original manuscript. A 78 RPM record by Burl Ives immortalised this mistake in 1944, incidentally enabling us to track later recordings of the song from traditional singers back to the Ives recording if they include the She-Devil line. So there's that.

But there are also examples of genuine shared tunes between British and American singers, of course. Like The Douglas Tragedy (Child 7) which was sung by Robert Henley Shiflett (1903–1978) of Brown's Cove, Albemarle County, Virginia, USA. Recorded by George D. Foss on July 15, 1961. And by Betsy Whyte (Bessie Townsley) (1919–1988), a Traveller of Montrose, Angus, Scotland, around the same time. Different words, but very close tunes.

Or "Young Hunting" (Child 68) aka "Lady Margaret". Sung by Martin McDonagh, a Traveller of Lanabawn, Roscommon, Co Roscommon, Ireland on May 22, 1974. Recorded by Tom Munnelly. And "Song of a Lost Hunter". Sung by Frank Proffitt of Watauga County, North Carolina. Recorded by Frank Warner in 1959. Completely different words, but clearly variants of the same tune.