In a wide, heavy saucepan, heat the oil over moderate heat. Add the onions and celery and sauté, stirring, for about 7 minutes or until softened and lightly browned.
Stir in the barley until well coated with the oil. Pour in the stock and add the lemon zest, oregano and pepper.
Bring the stock to the boil, then reduce the heat, cover the pan and simmer, stirring occasionally, for about 40 minutes or until the barley is nearly cooked and almost all of the liquid has been absorbed.
Meanwhile, toast the sunflower seeds in a dry non-stick frying pan over moderate heat, stirring frequently or shaking the pan, until they are golden brown. Remove from the heat and transfer to a plate.
Stir the lemon juice and sultanas into the barley mixture. Cover the pan again, remove from the heat and leave to stand undisturbed for about 5 minutes.
Gently stir the toasted sunflower seeds and parsley into the barley. Serve hot.