I think 'of England' is less capable of misinterpretation than 'English'

I don't think that's right, as your mention of John Doonan illustrates. I don't know whether he thought of himself as English, Irish, Geordie, a mixture of any of those, or something else entirely, but his music was undoubtedly Irish. He played it in England, and so it could be said to be "of England", but it would be a brave person who claimed it to be English music.

There is a large Irish community in most parts of English which vigorously promotes its own musical culture. There are many other communities with their own traditions, which could also be said to be "of England".

EFDSS has never confined itself only to English music and neither has the wider folk scene. That's one thing, claiming to be the custodian of all the folk music "of England" (as one of the survey questions suggests) is quite another.

Perhaps this too is a pedantic interpretation, but it shows that the meaning of both phrases is unclear. The problem is that, however you interpret it, Englishness is at the core of EFDSS's purpose, and it is tying itself in knots trying to avoid saying this.