Wogan once featured a live interview with a mudcatting person during which Jour d'Eté was played on concertina (very nice but not exactly f*lk whatever that is). He did remark when the tune was over that he thought it would never finish though.

FWIW, Mark Radcliffe often plays tracks from the Smoothops end of the genre. But if you're looking seriously for English trad on the BBC, R2 is scarcely the place to look. R3 & 4 are considerably more fruitful.