I don't know
I remember several quite early gigs, but don't know what order they came in.
I definitely knew who they were before the first Oxford Folk Festival in spring 2004 - in the run-up to that Bellowhead were billed as "The Spiers and Boden Big Band".
I remember a gig at the Cellar in Oxford in late 2003, and I remember buying Bellow in the interval before they played, so I must have at least known who they were before that. I also remember being worried about Jon using a stompbox on stage... If you know the Cellar you'll know why - when Jaune Toujours played there, the double-bassist managed to wedge his instrument between floor and ceiling!
I also remember around this time seeing Eliza & Co at the Zodiac on two separate occasions a year or two apart and I think J&J played at both. They were definitely at the second of those gigs and I'm certain that I'd already seen them by then and knew who they were. I remember they were out selling merchandise with Eliza in the interval (I bought Through and Through from Eliza - I felt a bit embarrased about that but I already had everything of hers she had for sale), then they went off and played a short set straight after while Eliza got a broom out and swept up all the discarded CD wrappers!
I'm pretty sure they played at the first of her Zodiac gigs too - I recall Eliza stepping to the side and letting a couple of the band play some of their own songs mid-way through the set. So I'm going to go with that: J&J as part of Eliza's band, at the Zodiac around about 2002.
(I am at least a bit clearer about the first time I saw Eliza in her own right. Glastonbury 1998, in the New Bands Tent. I had just left a tropical island (Kaua'i) the week before and had literally travelled half way round the world to camp there in the pouring rain and mud... That said, didn't she play Cropredy years before that?! I would have seen her at Cropredy for sure! Dammit my memory