We are fortunate to have three places (plaices?) two of which have restaurant facilities.
The ones where you can eat in or takeaway are Scalinis, on Wrawby Street, and the Hungry Fisherman, down Coney Court.
The Garden, on Grammar School Road, is the other chippie of note.
Of course, you can find "one of each" on offer at various Brigg eateries which do not restrict themselves just to fish, including Wetherspoon's White Horse pub/restaurant.