The Orangery is not famous only by its tea and cake, it is mostly noticeable because it is located in the centre of Kensington Palace Garden, a very fine garden besides the ugly Hyde Park. You can get a table outside of the building and sit in front of the beautiful sight all afternoon. Very nice!!!! The cost is not high neither. It is definitely more worthy than going to the Fortnum & Mason.
A few photos of my classmates here.