First, let's wind the clock back: market rights in the City of London were based on a charter granted by Edward III in 1327, with rival markets to those in London being prohibited from setting up within 6.6 miles of the City (the distance a person could be expected to walk to a market, sell his produce and return in a day). While the original Billingsgate market traded corn, coal, iron, wine, salt, pottery and fish, sometime in the mid sixteenth century it became exclusively a fish market. The first purpose built market was constructed on Lower Thames Street where the building still stands (though is currently used for parties, conferences and the like) but in 1982, the market itself moved to Canary Wharf onto a dedicated 13 acre site. Pictures old and new are shown below (indeed, if you are on Lower Thames Street, look out for the fishy weathervanes on top of the building and other fish motifs that adorn the building).
On that note, some market stalls are packing up to leave by 7am (the market itself shuts at 8:30am) and the best of the fish clearly sell first so it's worth getting there early. Also, while the floors have built in drainage, it can be pretty ruinous for shoes or trousers that drag along the floor (unless you like the permanent smell of fish attached to your clothing) so appropriate footwear is advisable. Parking is free and plentiful and off you go. Oh, final tip, watch your back, there's loads of pallets and crates being constantly moved and not every porter is that concerned whether you're in the way or not (like London bus drivers really). Stay aware.
The stalls are all competing with each other so it's worth checking the whole of the market for what you want and buying it where you find it most attractive either on price or quality. We picked up a fantastic 1.7kg wild sea bass (around £11 per kg) that was so fresh its eyes were shining. Four crabs (about £10 for the four) and a kilo of supersize Indian Ocean shrimp. You'll probably have to buy greater quantities than you'd normally buy because while they do sell to retail customers, it's a wholesale market more than shop but here the good news is that the price is sufficiently cheap (no middle man mark up) that buying more still costs you less.
So it was up at 5:15, the market for 6. An hour there, after which a cat-nap followed. Just a few hours on, crab cakes and poached egg for lunch, wild sea bass on a bed of greens for dinner and later that weekend, with the sea bass bones and prawn heads having contributed to a fish stock, we had prawn and crab risotto with asparagus. All washed down with a nice white burgundy. No brainer that it beats going to Tesco, but it also beats your local fishmonger (who probably bought his fish there any way) or indeed Borough Market for fish though as noted, you wont get advice or help with prep at Billingsgate.
A cracking morning out though. Billingsgate is open Tuesday - Saturday, 5am to 8:30am.