Do you know where you will live? When I lived in London, I found it to be truly a series of small villages. I was very local in much of what I did. Fortunately, I lived very centrally in London, in W1.
My fave place for afternoon tea, after much serious sampling

is the Dorchester. Some of the places, such as the Ritz, have set times for tea. Others, such as Browns, serve everything all at once on a 3 tiered tray. The Dorchester understands it is all about comfort and unwinding. They have squishy chairs and sofas, and let you wander in whenever you want. You are served finger sandwiches til you want no more. Then come the scones with clotted cream. And finally come the pastries. It is wonderfully relaxing, with a pianist playing softly.
I left London 10 years ago, and still consider a stop at the Dorchester on trips back essential.