London is so vast I am forever coming across new hidden gems. Walking around the streets and getting lost is the best way to find London's best kept secrets.
A great place to start the day if you are in South London is Federation Coffee in Brixton Village. The food is great and so is the coffee. This is a very chilled place where you can get both and indoor and outdoor experience (even though the whole place is under the Village roof).
If you like some nice cool beer, portuguese sweets (the once with yellow custard inside) tasty and affordable sandwiches, good strong coffee and football, at all hours. Max Snack Bar is worth checking out.