Place the cod, breadcrumbs, egg white, shallot and basil into a food processor and pulse until combined, but not pureed, then season with salt and freshly ground black pepper.
Divide the mixture into four portions and shape each portion into a burger shape. Place onto a plate and transfer to the fridge to chill for 30 minutes.
Heat the oil in a large frying pan, then add the burgers and fry for 3 minutes on each side, or until golden-brown all over and completely cooked through.
Mix together the ingredients for the sauce and heat gently in a saucepan, stirring until thickened. Place the lettuce in the bun, then the fish burger and top with the sweet and sour sauce.