The following information is not exhaustive nor comprehensive. It is based on a brief phonecall with Brighton & Hove FareShare manager, Nathan Au at the beginning of 2013. His overiding comment was that he understands that the demand is far greater than the supply of food could currently address:

There is one full blown Foodbank in Brighton coordinated by Brighton & Hove City Mission from their premises near Preston Circus. It is known as the Basics Bank. 

There are several other schemes operating which provide food to inviduals in a more localised or targetted manner. These are believed to include:

Terence Higgins; Brighton Womens Centre; Salvation Army near the Level; Brighton Unemployed Centre, Tilbury Place; Fresh Start community centre. There are also some schemes operating out of some of the Sure Start Centres across the city.