We stayed here recently, my husband, 4yr old and I. We had a great stay.
We wanted to stay in Peckham specifically to experience South London...mainly for the food and to stay away from tourist traps. The authentic Indian, Kurdish, Jamaican and Middle Eastern food didn't disappoint. There are also some great coffee shops with excellent coffee.
Super easy access to the train line.
A beautiful and bright apartment with greenery everywhere and the most comfy towels!