Sussex is pretty well serviced for food, every town has at least one supermarket with almost every village have a pub or public house, food is to the standard of the rest of the UK, with a greater variety in towns. Brighton and Hove prides itself on having a vast cultural array of foods, from Mexican to McDonald's and from Chinese to Celtic. Specialist diets vegan, vegetarian kosher etc are well supported, although in the countryside and surrounding towns there will only be one or two albeit very nice vegetarian dishes on the menu
It is highly recommended to visit a farmers shop or market, since produce here is generally much better quality and often a lower price than supermarkets. Most towns will have a farmers market at least once a month. Farm shops are dotted around the country:
Boathouse farm shop
On the a26 north of lewes
Middle farm shop
On the a27 east of lewes