After staying at Elaine's, I'm re-thinking how often I give 5 star reviews. I'm only giving them out from now on for places that are of the same caliber.
First, the area - The place is very central, an easy walk to London Bridge, there are local cafes, and the area feels very, very safe. It is near the river, and has a very upmarket vibe. If you are a tourist you will want to stay here.
Next, the room - the room is lovely. The bed is very high off the ground, which honestly makes it so much more memorable than any other bed I've been in. It is also very firm, which is great if you have a bad back. The room has a kettle, which I used for teas, and a lovely large window with a sunny view. It is very nice.
The apartment has a separate bathroom and shower-room, both were always extremely clean and well kept. There are three cats, who seemed terrified of me and I rarely saw them.
Finally the hosts - Elaine and David are lovely, easy to talk to and very friendly. I found them to be helpful, engaging, charming and otherwise lovely.
You really need look no further than this place - it is one of the nicest places I have been in using Airbnb, and is miles ahead of any place I've used for London.