The questionnaire does seem to be designed to produce the answer they want. There is no opportunity to vote on the name itself, although you can add comments.

I think the survey they did on "Englishness" was misguided and asked the wrong questions. The answers are all about people's sense of self-identity. However whether or not one enjoys a genre of music is primarily an aesthetic choice. It may help to feel a personal connection with it, but it is not necessary in order to enjoy it. English music is played around the world, often by people with no connections with England. There are morris teams overseas, and they are not all English ex-pats. Somewhere on Youtube is a video of an English music session in Japan, with Japanese musicians.

This is even more true of Irish music, which has a strong following all round the world (also including Japan), well beyond the Irish diaspora. Back home, I know English musicians who play Cajun and Zydeco, klezmer, French and Scandinavian music who have no connections to any of them. It's just music. Do you have to be German to enjoy Bach?