I think as it's placed in that sentence 'other folk music' is more likely to be there to include English folk music other than songs. If not English folk music other than songs is not included. In the other objects it is condensed to "ENGLISH FOLK DANCES, SONGS AND MUSIC, TALES AND DRAMA" and in the last one that is distinguished from "THOSE OF OTHER COUNTRIES"

If by 'other folk music" they meant the folk music of other countries then I think, given the name of the charity, they should/would have said that.

If that's what's meant (now, whatever it meant before) there is no reason to rely on a possible ambiguity, they could just change it to be more explicit. Though since they have members I think the trustees would have to ask the members' views. And I bet some would not agree...