The Arts Council of Wales has for long time had a policy of funding which does not exclude folk events, particularly through their Night Out scheme. Llantrisant Folk Club (I can't speak for other clubs) has in the past had grants for particular events from the Arts Council in partnership with our local authority.
I believe the the English Arts Council has a new venue development scheme for bringing the arts into areas that are under-served. I know, for example, that Sid Kipper works a lot through this scheme.
You need to develop a working relationship with people from funding bodies, who despite criticism regarding "high" art, are there to help you. Don't go in just demanding money, but ask questions regarding how they might help you develop an audience/venue. You may have to adjust your thinking a little bit, but it won't compromise your primary aim which is (I'm guessing here) to spread your music etc as far and wide as possible.
Remember you are dealing with people, not faceless organisations.

Splott Man