Out of a handful of places to get your coffee from in London, Monmouth is usually mentioned. Past the line is a large communal table for you to enjoy your coffee and a croissant perhaps, which can be selected from the buffet style tables toward the back.
You can both buy a coffee and your beans here. It is also here that you'll soon understand why Monmouth are pioneers for the pour over. It's a must stop before or after a venture to the Borough Markets.