Sift the flour and salt into a large bowl. Make a well in the centre and gradually add the beer and cold water, whisking to form a smooth batter. Cover and leave to stand for 20 minutes.
Fill a deep, heavy-based saucepan one-third full of oil. Heat the oil to 160C, or until a bread cube dropped into the oil browns in 30-35 seconds. Add the potato, in two or more batches if necessary, and deep-fry until tender, but pale in colour. Drain on paper towels.
Heat the same oil to 180C, or until a bread cube browns in 15 seconds. Cut each fish fillet in half diagonally and pat dry with paper towels. Dip the fish in the batter, gently shaking off the excess. Deep-fry for 3-4 minutes, depending on the thickness, or until crisp, golden and cooked through. Drain on paper towels.
Reheat the oil to 180C and gently return the chips to the pan. Cook for 1-2 minutes, or until crisp and golden. Drain on paper towels and serve with the fish.