I would highly recommend that you consider staying at Will's Battersea apartment. Unlike many options in London, this is a genuine home with kind, pleasant hosts living on site. They are more than usually welcoming and clearly want to help their guests' to make the most of their time in London. There wasn't a destination that I visited that Will and Irena were unable to give me directions to. They are London transport experts! And the buses do work well - sometimes more reliably than the tube.
The location isn't perfectly central as you can see from the map but personally I found the daily commute across the river refreshing and interesting. It was nice to see a horizon and hear the gentle padding of the waves.
My stay was 8 nights for a work trip. I was very pleased with my accommodation choice.