One of the famous food markets in London is Borough Market. The closest tube station to this market is London Bridge; coming out it is to your right. You can either turn right towards the wall and go into that entrance, or you can turn the first corner and hit the market that way.
The market is full of fresh fruit and vegetables, organic butchers and various specialties when it comes to meats and confections. There are also a good amount of food stalls. The market isn’t that large, but you will miss a good part of it if you do not go down all the winding alleys in the market. There is also the “green market” which had mostly cooked goods and the food stalls.
While I was there I bought some chicken livers (not bad at 7 pounds a kilo; I bought about 2 pounds worth and it was enough for two meals) at a stall called “the ginger pig” and a steak and kidney pie for lunch. I got it at Pieminister. The pie was the “Kate and Sidney” and came warm with gravy on top for 4 pound 50. The filling was fantastic, tender and with good flavor. The crust had that British quality of being solid and a bit bland and meant to just keep the filling in. The gravy for me was a bit “meh”, it was just a generic beef gravy for all their pies involving beef. This stall was also near the famous toasted cheese stall, which my flat mate had been thinking about but it didn’t look that great and was a bit much for 5 pounds.
Overall, I’d say borough market is a good place to stop by if you happen to like hand pressed olive oil and pigeon breast and are south of the river. If you are planning to spend your entire evening or if it is really out of your way, maybe try to check out another of the many markets in London.