Remove the skin and bones from the fillets. Cut the fillets into chunky fingers and allow to come up to room temperature, this will ensure a more even cook. Place the fish fingers on a flat dish and coat them with the seasoned flour, making sure they are well covered on all sides.
Place the beaten egg and breadcrumbs in two shallow dishes then dunk the fish in the egg, then into the breadcrumbs, ensuring they are well covered on all sides. Shake to remove any excess crumbs.
Pour a sufficient amount of sunflower oil to fry the fish into a large frying pan. Warm the oil over a medium heat then add the thyme. Once oil starts to sizzle, add the fish and cook for some 3 minutes or so on each side until crispy and the fish is evenly white and flakes with a fork. Remove the thyme sprigs and discard; season and serve immediately.