How about the Promenade at the Dorchester Hotel? From memory they do have comfy sofas and it’s very fancy. http://www.thedorchester.com/
Or for something different, you could opt for a one of the luxurious booths at the Met Bar (Metropolitan Hotel). The afternoon tea is called Afternoon Delight and it’s really lovely. http://www.metropolitan.london.como.bz/eat-and-drink/afternoon-de-light
