Karen wrote:

'Songs from the Collection of Mr Frank Kidson, Folk Song Journal (English), 1904'... may be the actual origin of the myth that there was an Irish version called 'The Unfortunate Rake'.

The writer says that the song is called 'The Unfortunate Lad'...
   
They give the tune, which is not the Unfortunate Rake tune. You'll have to play it for yourself and make your own judgment on this.

I did make my own judgement, using the Vaughan Williams Library Online Archive. There you can see an image from Kidson's original notebook, where he transcribes the song beginning 'As I was a walking in Rippleton Gardens' and remarks on the similarity to 'The Unfortunate Rake' tune as printed in 'Crosby's Irish Minstrel'.

Lucy Broadwood (who co-wrote the FSJ paper with Kidson) provided an additional comparison of Kidson's collected tune with 'The Unfortunate Rake' from Kerr's'Merry Melodies'.

I'd have said that the two melodies have a lot in common. The first three bars are pretty near identical.