Moving to London, looking in SE London

I’m starting a new role for a Council in London, and I’m looking for somewhere to live in around the southeast of the city. I'd like to be able to move in during the first week of September, if possible.

I do value alone time, though that definitely doesn't preclude living with more extroverted people and I am certainly not a hermit. I like to read, am trying to get good at running and spend a surprising amount of time listening to the radio. I'm also learning how to play the guitar, but I make a conscious effort to keep this to very reasonable times, and reasonable sound levels.