Fleet Market
The Fleet Market was a London market erected in 1736 on the newly culverted River Fleet. The market was located approximately where the modern Farringdon Street stands today, to the west of the Smithfield livestock market.

The Fleet Market was a London market erected in 1736 on the newly culverted River Fleet. The market was located approximately where the modern Farringdon Street stands today, to the west of the Smithfield livestock market.
Check the official site before travelling; hours and prices can change.
More markets

Borough Market
London's defining food market — go early Saturday, eat your way around the perimeter.

Columbia Road Flower Market
Sunday-only flower market in the East End — 8 a.m. for choice, 2 p.m. for prices.

Maltby Street Market
Borough's smaller, scruffier sibling — railway arches, weekend only.
Source: wiki-list