I highly recommend Jen's place. It is 2 blocks to the tube, across the street from Tesco, and within walking distance of Borough Market and Tate Modern. It was very clean, spacious and comfortable. Thoughtful touches like wooden hangers in the closets, tea in the cupboard, a decent blow dryer, and good sheets made it home away from home. Bonus marks for good bedside lighting for late night reading for those with jetlag!
My girlfriend and I stayed for 3 nights as a getaway and it was perfect. Even though I won the coin toss and got the bedroom, which was very inviting, she reported that the sofa bed was also comfortable.
I hadn't explored the Bankside/Southwark area previously, and it was a positive experience - we felt a bit less among tourists. We discovered lots of neighborhood cafes and shops, including the small but interesting Fashion and Textile Museum.