Depends what you call a club, and what you call folk. There is a certain case to be made for Bunjie's coffee house in Lichfield St, near Leicester Square. This has been going since 1954 and has been host to many musical luminaries over the years (OK, I admit I used to do the late shift on Saturday nights in 1975, but I'm not on their list of favourites). Whatever the case, it has always been a commercial venture with an (almost) paid musician as a host for as long as I've known it, but floor singers have always been welcome and folk music has always been performed most nights.