There are currently two 24 hour off licences in the London Borough of Camden:
Sainsburys, O2 Centre, 255 Finchley Road, Swiss Cottage/West Hampstead, NW3 6LU - 020 7433 1493 (No longer open 24 hours!)
Sainsburys Local, MidCity Place, 71 High Holborn, London, WC1V 6EA - 020 7404 9406 (Not currently open 24 hours)
As both of the 24 hour off licences in Camden are not open 24 hours a day, there isn't anywhere you can legally buy alcohol all night in the London Borough of Camden. If you are in Camden, the only legal way to buy booze after hours is to travel to a 24hr off licence in a nearby borough or try one of the many companies now offering late night alcohol delivery in Camden and other parts of London.
Please Note: Just because a shop is listed as having a 24 hour alcohol licence doesn't necessarily mean that the shop is open 24 hours a day, 7 days a week. It's up to each individual shop to decide whether or not it uses its 24 hour alcohol licence (just because they are licensed to sell alcohol 24 hours. It's also worth noting that large 24 hour supermarkets (Tesco, Sainsbury's and Asda) are not open all night on Saturday, Sunday and bank holidays (due to Sunday trading laws in England and Wales), so are only of any use on weekdays or Friday nights. We've tried to list the phone number for each 24 hour off licence so you can confirm opening times before setting off on your quest for 24 hour booze.