To make the batter, whisk the self-raising flour, salt, beer and water together until smooth. (This can be also be done in a food processor; transfer the mixture to a large bowl for dipping.) Cover and stand for at least 30 minutes, or up to 2 hours.
Meanwhile, cut the potatoes into chips about 5 mm thick. Put them in cold water for 5 minutes to remove the excess starch, then drain well and pat dry on a clean tea towel.
Half-fill a deep-fryer or large, deep saucepan with oil and heat to 195°C. Blanch the chips, in two batches, in the hot oil for 4–5 minutes, or until very pale golden. Remove from the oil, drain well on paper towels and set aside.
Allow the temperature of the oil to drop to 175°C. Coat the fish lightly in seasoned flour. Stir the batter vigorously and, using tongs, dip two fillets of fish into it. Lift out the fillets and allow the excess batter to drip back into the bowl.
Carefully lower the fillets into the hot oil, submerging them with the tongs, and cook, turning once, for 4–5 minutes, or until crisp and golden. Using a large wire skimmer or slotted spoon, lift the fillets out of the pan and drain on paper towels. Keep warm while dipping and frying the remaining fillets.
Increase the oil temperature to 200°C and fry the chips for 2–3 minutes more, or until crisp and golden. Drain well on paper towels and season with salt. Arrange the fish and chips on heated plates and garnish with the lemon wedges. Pass some full-flavoured vinegar separately.