The Fig & Olive in Islington is a busy venue with a nice friendly buzz. The cakes displayed by the door (which are also available as take away), look stunning, and if the bakewell tart I had was anything to go by, tasted good too.
This is not just a venue for Coffee and Cakes though. They also have a varied menu covering everything from English Breakfasts to Sunday Roast, and a selection of wines and cocktails.
Unless you are in an area that specialises in Tea Shops, its often hard to find good venues to relax with a coffee or tea and eat cake. Why go to the big chains like Starbucks, when you have alternatives.
London
If you really want to go up market and have Afternoon Tea somewhere grand, like The Athenaeum or The Berkeley, then great, but if you are looking for something cheaper, then here are a few options.
Actually the Starbucks I have been to in New York are a lot better than London. I had an amazing piece of Cognac and Pumpkin cheese cake in one on the Upper East Side, but for something more unique try:-