Harrod's food court has lots of take-aways and I'm quite partial to that extensive food court. It truly IS amazing; as are the lunch counters and restaurants!
Simpsons has quite an extensive menu, never had a bad meal there and their roast beef dinner is fantastic! If/when you go to London, you really should try it.
Over the years, we've dined at several different restaurants in London's China Town and every single one of them were perfection. The first time that we were brought the finger bowls with tea and a lemon slice in them, we were surprised. In America, long ago, top Chinese restaurants did also bring out finger bowls, but they were filled with warm water and a lemon slice...not warm tea. But the tea does work well on greasy fingers. Sadly, I don't remember the names of the Chinese restaurants we ate at. :-(
Marks & Spencer is known for Jumpers (sweaters), Underwear, and a Grocery Store where they have containers of prepared food that just need to be baked at home.
We lived in Kensington and never have eaten so well!