OK, I’ve been checking. I actually have three recordings of this tune (at least that came promptly to hand once I knew it was Northumbrian) and a setting of it in a book. The written version I reproduce in ABC below exactly as it appears in The Northumbrian Pipers’ Tunebook published by The Northumbrian Pipers’ Society (save for having “tr” marks instead of shake signs) of which I have a copy.
T:Sir John Fenwick’s The Flower Amang Them All
C:Traditional
O:Northumbria, England
S:Northumbrian Pipers’ Tunebook (1970)
Z: Jem Hammond 8:7:2008
M:3/4
L:1/8
K:G
G3 ABc | d2 e2 g2 | d2 e2 g2 | edcBAG | A3 B cd | e2 e2 g2 | e2 e2 g2 | Te4 d2 | G3 ABc | d2 e2 g2 | d2 e2 g2 |
edcBAG | c2 dcBA | B2 cBAG | A2 B2 d2 | Te4 d2 :|]|: g2 G2 B2 | g2 G2 B2 | g2 G2 g2 | edcBAG | a2 A2 c2 |
a2 A2 c2 | a2 A2 a2 | Te4 d2 | g2 G2 B2 | g2 G2 B2 | g2 G2 g2 | edcBAG | c2 dcBA | B2 cBAG | A2 B2 d2 | Te4 d2 :|]

That is essentially the version Kathryn Tickell plays on the recording Colomon mentions, which I have. It is also what small-piper Richard Butler (who these days lives near me in Wrexham) plays with some virtuoso variations on the 1999 Nimbus Records album Spirit of the Border (which also features another piper, Adrian Schofield, who occasionally turns up at my local session - so that’s probably why I have played it in recent years… shifted to D from G as he has a hybrid D chanter he uses in non-Northumbrian session contexts). I don’t know (yet) if it was on one of KT’s early albums as I don’t have them, though it is possible the old friend whose copies I once heard may still have 'em - I’ll be asking!
Finally, my original encounter with the tune, and the influential (on me) setting of it that, I think you’ll agree, is very close to my unresearched recollection, differing in some details from the Piper’s Tunebook standard version (oh, the aural tradition!!!), was in this recording by 1970s Geordie band Crooked Oak, whose late 70s or early 80s album (it has no P date anywhere on either vinyl or sleeve) The Foot O’Wor Stairs features it. I also saw them live in Cardiff a couple of times around then. That was my first encounter with Northumbrian small pipes, which were far more an obscure curiosity then even in the folk world than Irish pipes. OK, I’ve changed the key signature and some of my details are kinda fixings of what are really variations on the original in Crooked Oak’s setting, but you can still see/hear where I was coming from.
I think this is an interesting example of how tenacious of precise details of melody the mind can be even over quite long time-spans, and how influential on that memory the first-well-known version can be. Now my recall has been stimulated, I can even remember listening to the KT version and thinking “Oooooh, that bit’s different from how I know it”. Of course, I’m at least as bad at remembering tune titles and original contexts of knowing them as I good at remembering the melodies!

Thanks again guys - you got me on the right track.
ADDITION: OK, now I know what I’m looking for, it is there on the main ABC sites - just I was looking for it in the wrong key and didn’t think to use the transpose search functions - dur! There’s loads more info about it here on Fiddler’s Companion.