The reverse is the case. A P Graves (1846-1931) wrote a lot of songs incorporating or based upon traditional and/or older material, and this is one of them.

An earlier example of 'Herring the King', beginning 'Of all the fish that roam the sea', was published in Horncastle, Music of Ireland, I, 1844. It has a rather literary flavour, and was probably itself worked up from older material. It is re-printed in Alfred Moffat, Minstrelsy of Ireland, 1897, 168-9. Moffat notes:

'... As "The Brink of the White Rocks" the tune was published four years earlier in Bunting's third collection; Bunting states that he obtained it from a blind man in Westport in 1802. An ancient air called Thugamar fein a samhra lin; or, "We have brought the Summer with us," is printed in Bunting's Collection of 1796. An earlier and probably more genuine setting of it is to be found in Burk Thumoth's Twelve Scotch and Twelve Irish Airs, London, c.1745, entitled Hugar mu Fean, and another as Hugar mon fona souraling, in Mulhollan's Irish Tunes, 1804. The air adopted here has all the appearance of antiquity. Dr Petrie gives four settings of it in The Ancient Music of Ireland ...'

The set in Healy seems to have been copied from Horncastle or, perhaps more likely, from Moffat, not from tradition as he implies. The words are identical and the tune is even in the same key. Note, however, that much of the material in Healy was copied without acknowledgement from Father Joseph Ranson's Songs of the Wexford Coast, so that too may have been involved.