My favorite places throughout London where you can sit down with a laptop, have some sort of Wifi and be ok with looking at your screen for extended periods of time.
Roman Mittermayr: Go straight through to the bar at the end, ask for an espresso (at an Italian price, so great!) and sit upstairs in the quiet roof garden.
Roman Mittermayr: Go there before 5pm and it's so quiet you'll hear your fingers hitting the keys on your laptop keyboard. Go after 5pm and you won't have a chair.