One thing in the fringe that has been recommended to me is Camille O’Sullivan. It looks a nice mix of cabaret, burlesque and pretty good music. It might be worth a visit, if you’re into that sort of thing. Warning: from the look of the video, there’s a good bit of crowd interaction. She sings a good chunk of this song on the lap of one of the audience!
Below, her version of a good man is hard to find, by Tom Waits (from the album Blood Money).
No More Workhorse 
I saw her sing a few songs at a Jacques Brel tribute thingy. She was good fun. Crowd interaction sounds scary tho.
yeah, a lot of people just freak out when anyone from the stage comes near them! Try to sit in the middle of a row, and then you’ll be fine..