There used to be a truly cosmopolitan jazz session at the King's Head, Crouch End (N8), Sunday lunchtimes - great atmosphere, and better than most of the Irish/folk sessions I ever found. I'm not in London anymore, so check first. Also bluegrass (Pete Stanley & Co) at the Stick & Weasil(spelling?) near Angel (City Road I think), again Sunday lunchtime. For Irish traditional, try Biddy Mulligan's at Kilburn and the Irish Centre, Camden.