tweet from Saveur about where to eat, drink, and stay in London, I found The Wolseley. Here's what Saveur said about it:
"This glamorous Art Deco grand café in the Parisian or Viennese tradition, all black marble, gold accents, and soaring ceilings, was originally an automobile showroom when it opened in 1921. Antique Orientalist décor and mismatched silver-plated teapots are part of the Old World charm. It’s a fantastic choice for breakfast or afternoon tea, but an all-day menu of elegant European dishes is available till midnight."
The Wolseley was walking distance from our hotel and offered afternoon tea until 6:30 pm at a cost of 26 GBP per person. We made reservations for 6 pm on a Sunday after a day of sight-seeing in Greenwich. We ended up a little rushed to get there on time because the boat ride back from Greenwich took some time and then many roads and crosswalks in the area were blocked off for a bicycle race so we had to backtrack a lot and go the long way around a lot. It was kind of frustrating, and tiring.