Our one week in London we had booked an apartment in Westminster. This one bedroom (+den) penthouse flat of a small apartment building (Victoria One) had full service kitchen with all tools and gadgets you could wish for, washer/dryer and a dining table. The apartment had beautiful hardwood floors except in the bedroom, heated bathroom floor (yay!), towel warmers and a huge balcony.
Den with sofa bed and desk for working. Perfect for bringing the entire family!
We liked the quiet area. It was fun to walk in the empty streets at night. We basically walked everywhere from here: the Piccadilly Circus, River Thames, Soho, Buckingham Palace etc. So much walking. Felt good.
We also had free wifi, but it was not working too well. I would definitely stay here again if we come back to London!