This is a great location with warm, kind people and gorgeous cats. You are in an upscale edge of the ultra-luxe Battersea development, on the edge of a working class neighborhood, have good transit into London proper. We missed the New Covent Garden Market Sundays, but it really it's just right down the block. Oh, great coffee, comfy bed, spacious feel in the 5th floor unit, and a heated towel rack (swoon!). Dem is a terrific host.
Quick notes: Our navigation wasn't accurate. One trick may be to navigate to Matt's Gallery. The building is across from it at the street front. Once you receive the address, what looks like a street number is the unit number.
Also, it seems like every other Northern line train don't stop at Nine Elms at least in the evening though it's not clear. The next train comes soon enough, but you may want to ask Dem for clarification on that bit of the southbound route.