Just got back from Lucy and Glyns place in Pimlico. Lovely basement apartment and wonderful and thoughtful hosts. The apartment is fully loaded and has all you could ask for from washer and dryer to a refrigerator and microwave. The location is wonderful with access to Pimlico and Victoria lines and one could walk to Tate Britain and the lovely antique stores at Pimlico. There is a corner grocery store and Tesco Express round the corner as well as bus access to many places in the city. Lucy and Glyn were super responsive, the check in process was smooth and as the hosts live upstairs any request was quickly addressed. Through it was cold in October the basement had space heaters and an electric blanket to warm me up. The place was pretty clean and wifi was great with a booster installed for good connectivity.
One note of caution, the entrance to the apartment has steep steps, which may be difficult to navigate by older folks or those with mobility issues. Though the hosts do help with carrying luggage down.
All the best!