Almost everyone goes to Borough market when in London, and it's also London's most known food market. I never get bored of it and make a stop there whenever I find myself to be in the area on the right day.
The market is one of my favorite places for lunch, with vendors selling almost everything you can think of and desire, most stands are pretty expensive but most times it's worth it. Open thursday, friday and saturday, the best day to go is on thursday so you avoid the tourists. My personal favorite is the oyster stand, with someone there to open them right in front of you, and you can sit down on the sidewalk next to the nearby church and slurp them down!