Azizi, not just that they could sing English folk songs, but also that English folk singers could sing *their* songs. If you go to an English folk club, songs like the Banana Boat Song, Sloop John B and other Afro-Caribbean songs are quite likely to come up, sung by white people. That's what I'd call integration. But it's *folk* style. There's a big difference between that and ska/reggae/dub.
It was obviously tougher for the Asian community to integrate, because there's a quadruple barrier of language, colour, religion and culture. Afro-Caribbeans at least shared a language and religion. But it's well under way.
As for Dave's comment that their club focusses on English folk music - well that's perfectly valid, if that's the parameters of their club. I wouldn't go to hear the London Philharmonic and complain about the lack of sitar music, or go to a blues club and play Irish diddly-diddly on a tin whistle. I like more variety myself so I probably wouldn't go to Dave's club if there was somewhere that mixed in blues and other acoustic stuff, but that's my personal preference, and it doesn't invalidate Dave's greater love for English folk music.
As far as "white folk music" goes, I guess mostly "commercial folk" in the UK and US has been done by whites, although there's been enough blacks involved too that this isn't a complete whitewash. If black people like the music and want to play, then I don't think there's ever been an obstacle (with the possible exception of music industry dinosaurs).