We just had a one-night stay at Charlotte's place, and we definitely recommend it. The house is in the heart of Catford, really close to Broadway theatre, where several shows and concerts take place - which was the very reason we were there. From there, it takes about 20-30 minutes to get to Central London by train. You can easily find bars, pubs and restaurants in the surroundings, and the borough itself seems to be pretty safe even at night.
Charlotte is a nice host. She gave us tips about places where having dinner or breakfast, and she was always kind and open to our requests. Furthermore, the house and our room were clean and well equipped, and the beds extra comfortable.
If you have to stay in South East London for few days, Charlotte's place should be your option.