I think you'll find it's G F# F E if you try it - at least that's what I play.

I did - to check before I posted. And G F E Eb is what I play. I first learned the tune off a Tinwhistle tutor which had a simplified version - G G G G. Later someone gave me some dots with the descending sequence and I am pretty sure that is what was on them. I remember the Eb particularly. Unfortunately I could not find the sheet with the dots on to check, though I had everything else from that source <Grrrrr>.

Either works and if some are doing one and some the other, you will get some interesting effects, though I doubt anyone really worries in a session.

A C/G melodeon could do it.

True, but most people in England have D/G melodeons. D/G 2 row melodeons often come with accidentals on the end button on each row. In such a case both sequences are possible with the D/G melodeon, though, in my experience, limited as it is, melodeon players usually do some interesting things with the left hand as well at that point.