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. Let me know if you have something I’ve not seen!

I'm pretty quiet day-to-day, and value me-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 an inordinate amount of time listening to the radio news, though usually with headphones. 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.

I start my job around the beginning of July, so would like to have something confirmed for just before then, but happy to talk timings.