I don't think it is appropriate to define Anglo by its American meaning when it's being used in England, Azizi. From Wiki:

"The term Anglo is used as a prefix to indicate a relation to the Angles, England or the English people, as in the terms Anglo-Saxon, Anglo-American, Anglo-Celtic, Anglo-African and Anglo-Indian. It is often used alone, somewhat loosely, to refer to the English people in The Americas, Australia and Southern Africa. It is also used, both in English-speaking and non-English-speaking countries, to refer to Anglophone people of other European origins.

Anglo is a Late Latin prefix used to denote English- in conjunction with another toponym or demonym. The word is derived from Anglia, the Latin name for England, and still the modern name of its eastern region. Anglia and England both mean Land of the Angles, a Germanic people originating in the north German peninsula of Angeln."

English folk music is largely comprised of the indigenous folk music of England. It is not considered by anyone I know as the only traditional music in England - from ska to bhangra, it's all here, and long may it prosper.

There is nothing wrong, as Dick Miles has insightfully pointed out, with having a society or group dedicated to a particular genre of music or dance. As long as that society is welcoming and open to people of all backgrounds, and they too, as Britons (whether naturalised or born here) are allowed to feel equal ownership over that heritage, I don't really see the problem. I also think it's important to look for natural points of convergence. I'm hoping to have a project at Sidmouth next year which will look at Caribbean and English mumming traditions. It involves bringing a group of Dominican and Kittitian mummers to Sidmouth. It also involves work in local schools looking at both traditions. For me, these are natural and organic ways of examining diversity: find the points of commonality and use them as an entry point into each other's cultures.

That doesn't mean I think every folk club or singaround should contain African Caribbean songs - in fact, when at my local singaround a bunch of white, middle class people start singing Let My People Go or Bob Marley's Redemption Song, I cringe. I'd rather clubs and folk events were simply open and welcoming to anyone from other cultures who wishes to explore them.