I can only recommend staying at Jessica's - It's a nice little place close to everything in central London. 2 underground stations 5 mins walk away, busses that will take you to Oxford Street /soho/St. Pauls or to Victoria station (just to name a few) 2 mins walk away.
The flat is surrounded with lovely middel eastern restaurants (The Indian restaurant across the street is really really good) and 5-10 mins walk and you are in shopping heaven on Oxford Street.
The flat it self is small, but perfect as a Base if you want to spend your time exploring London.
We were welcomed by Jessica 's housekeeper, who gave us a few tips on where to go and what to see.
Only thing to note if you are bigger than avarage is that the space the toilet is in, can be a tight fit.
We are happy to have stayed at the flat and would be happy to return some day.