'I have noticed in music sessions, tunes that I think of as English cropping up from Sweden, or Wales.'

No argument there, Mo. I remember 20-odd years ago being thrilled to hear a Danish band playing a tune I knew from Bob Cann as 'Double Quadrille' but which they'd got from their local tradition. The old English village tunebooks often have a few tunes with French titles, and there's certainly overlap with Northern Europe, Wales, and especially Scotland. But I would still argue that there is a recognizably English dance music repertoire, and style of playing it (like when Tex-Mex accordionists play 'The Beer Barrel' polka). The same is true even more for English songs.