Nell Gwynn House

These are «Luxury Serviced Apartments» located in the posh neighborhood of Kensington and Chelsea. It’s located between the South Kensington and Sloane Square tube stops, about a 10 minute walk to either one.
They have options for weekly or monthly stays.
The area can’t be beat — there’s a Starbucks, drug store, dry cleaners and a Sainsbury Local right across the street. Lots of great restaurants around the South Kensington Station. Over on King Street there are some nice shops and larger supermarkets (M&S, Waitrose).
I stayed here during a work assignment for a few months in one of their studio apartments. All the essentials were there — microwave, oven, stove, dish washer and clothes washer (although no dryer).
Maids came in to tidy around the apartment Monday through Friday.
If you’re staying in London for any extended period of time, this might be a better option over a typical hotel.