Put the potatoes in a pot of cold, salted water and bring to the boil. Reduce the heat and simmer for 15-20 minutes until they are tender. Then mash thoroughly. Beat in the butter and the basil and season well with salt and pepper and keep warm.
For the dressing, heat the oil in a pan and add the chopped shallot and garlic and sauté for 1-2 minutes. Stir in the tomatoes and wine and bring to a boil, then reduce the heat and simmer for one minute. Stir in the shrimp and season the sauce, then cook out for about 5 minutes. Set aside and keep warm.
Season the fish and fry in the olive oil in a hot pan for 8-10 minutes, turning half way through cooking time. Remove from the pan.
Place some basil mash in the centre of a place and lay the fish on top. Drizzle with shrimp dressing and serve immediately.