Farringdon Market
Farringdon Market was a market erected in 1829 in London, England, to replace the Fleet Market, which had been cleared for the widening of Farringdon Street and Farringdon Road. The market was between Farringdon Street east and Shoe Lane west, north of Stonecutter Street, in the City of London ward of Farringdon Without.

Farringdon Market was a market erected in 1829 in London, England, to replace the Fleet Market, which had been cleared for the widening of Farringdon Street and Farringdon Road. The market was between Farringdon Street east and Shoe Lane west, north of Stonecutter Street, in the City of London ward of Farringdon Without.
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