I had a lovely stay at Rima's, the room was cosy and clean and the flat well connected - a short walk to either NewX or pretty Brockley, both with over grounds and decent pubs and eats. Rima and her lodger Justin are both great to get along with and would recommend this place to solo travellers and workers alike.
... You'll have a much better time staying south London than a grubby joint in the centre for more money, I can guarantee it! ;)