According to "The Peel Sessions" (p236, under 2/12/96) this is the 4th show of the 2nd "Classic Sessions" Series (See also 1996-06-24). It comprises mainly cover versions.
Original recording date of each track give in brackets, along with source program if not John Peel.
Billy Bragg talks about his first session, where he revealed he heard John Peel feeling hungry for a mushroom biriyani on Kid Jensen's show, which prompted him to send a mushroom biriyani to the BBC and telling security that it was a delivery for John Peel, where Bragg left his LP with the meal to JP, who picked it up. Bragg also reveals that the BBC paid for his taxi when giving his first session.
Ted DeBono recalls Killing Joke recording their first session.
Thanks to Steve[TK] who "risked my hearing and my sanity" to identify three of the tracks.