Old Billingsgate Market
Old Billingsgate Market is the name given to what is now a hospitality and events venue in the City of London, based in the Victorian building that was originally Billingsgate Fish Market, the world's largest fish market in the 19th century.

Old Billingsgate Market is the name given to what is now a hospitality and events venue in the City of London, based in the Victorian building that was originally Billingsgate Fish Market, the world's largest fish market in the 19th century.
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