Thanks for your suggestions folks, but there are a few more details that I could, and maybe should, have added.

The track is definitely meant for dancing: a 2-note intro is followed by 9 x 32 reels, and a 2-bar coda. The band is accordion-led, possibly two accordions, plus two fiddles, guitar, bass and drums. No piano. Sounds English rather than American, as far as one can generalize about such things, and there is a great deal of "lift".

So it's not a Scottish band (they'd kick off with a chord), and not the Greensleeves band (whose lineup includes piano). Possibly the Ranchers or the Southerners, although the track's not on any of their records, or at least none of the ones in my fairly comprehensive collection.

If anyone thinks they have an idea but would like to hear the track to make sure, please PM me for an mp3 file.