Preheat the oven to 200°C/fan oven 180°C/gas mark 6. Lightly grease a baking sheet with a little vegetable oil.
Put the potato wedges into a roasting tin. Add the remaining vegetable oil and toss to coat. Season with black pepper. Transfer to the oven to bake for 35-40 minutes, turning them over after 20 minutes.
Meanwhile, sprinkle the breadcrumbs onto a large plate. Season with a little pepper. Dip each fish fillet in the beaten egg, then coat in the breadcrumbs. Place on the baking sheet, then transfer to the oven when you turn the potatoes, so that it cooks for 15-20 minutes. To check that the fish is cooked, it should flake easily when tested with a fork.