Borough Market next to London Bridge station. I've lived in London for fifteen years and until I started working at Bread Ahead I never really went there...I know, crazy! But it is south of the river and I'm a die hard north London girl. Borough Market has been around London Bridge, in some form, for almost 1,000 years!
Borough Market has dozens of stalls selling artisan foods like cheese, bread and meat. There are also fruit and veg stalls. There's a street food market next to Southwark Cathedral. I could go on and on about the amazing variety of stalls underneath the railways arches...but you really have to go there and see for yourself.
There are a range of pubs around the market, some of them hundreds of years old, where you can have a pintor two after a day shopping in the market.
Bread Ahead -for sour dough bread and donuts
Turnips - for fruit and veg
Fish! - for fish n chips
Boot & Flogger
The Royal Oak