Anyone checking out the food scene in London should visit the Southwark (pronounced suh-therk) Market, located on the newly-renovated South Bank of the Thames between the Southwark Cathedral and the new Globe Theatre. There has been a food market on this spot since 1016 A.D. It is under a lot of train tracks because when rail lines started coming into London they had to go around (over) this established market.
The market is open only to those in the food trade from Monday-Thursday and Friday morning. But Friday afternoon and especially all day Saturday it is open to the public. The produce and meats sold at the market are the best-looking I've seen in London and one buys direct from the producer (which is why it really is a farmers market).