Robin, to hear what it's like, give a listen to some of the files at Pilgrim Productions. I'm listening to the Minnesota Convention right now. A recording does not do justice to the experience of singing it, however.
I think you're in the UK. Stylistically similar is the West Gallery that's also been mentioned in the Unaccompanied thread. Some of the West Gallery people are also doing Sacred Harp. You can find out what they are up to HERE. I see there's a workshop in Haworth, West Yorks. on Saturday.