"Billingsgate is the market where the fishwomen assemble to purchase fish; and where, in their dealings and disputes they are somewhat apt to leave decency and good manners a little on the left hand." ["Dictionary of the Vulgar Tongue," 1811]
The place name is O.E. Billingesgate, "gate of (a man called) Billing;" the "gate" probably being a gap in the Roman river wall.