Brixton Market is hands-down the best place in London to have Sunday brunch.
Choose from any of the stalls serving grub from Mexican tacos to traditional English-style breakfast. I ended up at the Crepe restaurant the day I visited, and I loved the Asparagus omelette.
The history of Brixton Market is truly what makes this spot unique. Wikipedia gives a pretty decent description of its history, development changes, and use: http://en.wikipedia.org/wiki/Brixton_Market
After you finish eating, head out to the open markets that serve African foods, fresh fish, and Asian speciality items. If you aren't in the mood to grocery shop, just go for a stroll. This area is changing quickly, and lots of independent shops are popping up.