In the UK there are no traditional coffeehouses anymore after the 1960s. The concept has been revived since the 1990s by chains such as Starbucks, Coffee Republic, Costa Coffee, Caffè Nero and Prêt as places for professional workers to meet and eat out or simply to buy beverages and snack foods on their way to and from the workplace.
You can’t compare British coffeehouses to you what get in Paris or Vienna. Sad in a way, however there’s a market for that here. A place where you can rest from London’s pace.