The corporation, which owns and operates the central London site of the centuries-old market, had this month put on hold relocation plans to a new £1bn site in Dagenham to review the "financial sustainability" of the planned move.
The Court of Common Council, the main decision-making body for the corporation, voted yesterday to pull out of running the sites.
A market has existed around the Smithfield site for more than 800 years. The corporation was given the right to run it and other wholesale food markets in 1327 by Edward III.
The current market site was built in 1868, designed by the architect Sir Horace Jones, who also designed Billingsgate when it was redeveloped in the 19th century. The UK's largest inland fish market was moved to its current site in Poplar in 1982.
The corporation said it would provide compensation to traders, who will be able to continue their operations at the markets until at least 2028. Compensation could total more than £300m, according to the Times.
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