The market moved to its current site in Poplar, east London, in 1982, where it supplies fish to businesses, fishmongers, fish-and-chip shops, delicatessens and restaurants.
This site has been earmarked as the location for thousands of new homes.
Scott Unwin, who has been working for his family-run business for nearly 40 years, says the news has not yet hit home.
“It’s a shock and upsetting. I’ve been here 36 years and my boy is also involved in the business, so we’re all upset.”
Scott, whose father used to work at Old Billingsgate, added: “I left school at 14 and came to work as a shopboy with my father and we built the business up.
“Three generations in the business and it’s going to come to an end.”
He hopes a way can be found to “continue supplying London and Essex with the finest fresh fish in the world”.