Note that there are 7 issues of "Wild Rover" on the Bodley Ballads website and multiple copies of an 8th. All are by English printers, and it's no later than 1838.

Dan Milner, note that Frank Purslow was quick to identify any unknown good tune as Irish. He thought that's were most good English folk tune came from.

Origins ai going to remain a vexing questions for a long time. There is circumstantial evidence that the English knew and revised many Scots songs (Broom of Cowdens by c 1625-30). However they were revisted to fit contmporary tastes in England and one can pin down very well exactly what is Scots in some of them (Barbara Allan). Evidence is much more scant on Irish songs. "The Irish Lady" in the Dancing Master from 1651 is certainly Irish, because a version of it pops up later as "Teagues Ramble" The Teague song is Anglo-Irish and found on English broadsides, but the tune is not found in Enlish music sources. All Irish exept the earliest as "Nell of Connaught" in Oswald's CPC.

It's pretty obvious by looking in 18th century Irish songbook that the English in Ireland followed English tastes. It's difficult but far from impossible to find any (Anglo-)Irish songs. Gaelic was rare and it's phonetic Gaelic of extremly variable spelling that we get for tune titles, not songs, although researchs have found some of the original songs, but not from printed Irish sources. Gaelic speaking Irish weren't printers.

Give credit the the English for good taste; they devoured what was good no matter where it came from, and got some version published.

However, it seems to me that no matter the origin, it was to a large extent the British ballad printers that kept a lot of songs going, at least to the early 19th century (I only know of a MacGee as an Irish printer in the 18th century, and so far as I know all extant copies of his songs are in Harvard's collection).

There's a list of Irish broadsides in the huge Lauriston Castle Collection of NLS, compiled by Emily Lyle and published in (Eigse Cheol Tire) 'Irish Folk Music Studies', but all seem to be 19th century. The Bodleian Library also has a collection of ballads in Gaelic, but I don't know if they're Scots or Irish (and I've forgotten to look for them on the Bodley Ballads website.)

I'm afraid the battle of origins is going to go on forever, and we'll never find much solid evidence to prove anything.

Note that in a file on my website, I've made a case for an (Anglo-)Irish song being known in England in the late 16th century, "Derry's Fair" (a quarter century before Derry was given to London to became Londonderry). Also the tune "Braganderry" seems to be an undoubted corruption of a Gaelic title. Bragh and Breagh can mean several things and that part is far from certain (probably connected with false/toy/imitation or something close), and an daire is 'of oak' (Derry was named from it's oaks).

Take a look in my Scarce songs 1 file to see an Irish song and tune, "Pretty Peggy of Darby, Oh" that quickly disappeared in Ireland, only to turn up everywhere else, and it's was use as late as the civil war for a song on the battle of the Monitor and Merrimac (Song on Lib. of Congress recording- full text, naming same tune in Levy collection). (Bonnie Lass of Fyvie O". Well known "Scewball" has turned up in Ireland only in recent years, (and 18th century if not 17th) "Druimin Dubh Deelis" survived mostly in North America (Scarce Songs 1 again).

More than enough, I fear. Bye