As London’s oldest food market, Borough Market has been serving the people of Southwark for 1,000 years. Located next to London Bridge, the market is an easy location for breakfast or lunch. Favourite is Börek with home made hummus or a freshly made pasta dish.
It's really close to my house and one of my favourite pubs in London! (I even went before it was close to where I lived!) It is London's first cooperatively owned pubs and has lovely events and workshops, exercise classes and great parties, and good beer! It's lovely in the beer garden in the hot summer and equally great in the winter, next to a real fire.
Lots of traditional charming country pubs around the area, but it can a bit hit and miss. A really friendly one with amazing food (and a unusually large veggie selection…) is the Beehive in Epping Green; close to the Great Wood. It's friendly enough you dare going there by yourself with the paper and are not at the mercy of local rubbernecks ("the rubberneck" = person who stares at strangers without any sign of guilt)
A residential estate that once housed 40,000 people which has now become an abandoned ghost town. Minutes away from Elephant & Castle, is an unexpected dystopian treat.