I had such a lovely stay in Brockley at Davidandviv's place. The train was incredibly simple and quite close (I did not notice any train noise, despite the 5min walk to the station). it was very close to amenities, and incredibly easy to navigate into central London. it was a very safe area, and local enough that you don't feel like a tourist. the flat was perfect, minimalist, and very comfortable. I will stay here again the next time I'm in London.