First prepare the vinaigrette. Place the sugar and half a teaspoon of salt into a small bowl and pour in the lemon juice. Stir, then add the mustard and vinegar. Mix thoroughly then slow add the oil stirring continuously until combined.
Place the potatoes in a pan of cold salted water and bring to the boil. Cook until they drop easily from a small sharp knife. Cool quickly in iced cold water to stop the cooking and drain while still warm. Place into a bowl and toss in the vinaigrette. Cover and place in the fridge for at least two hours.
If you are adding beans, top and tail them with a knife and cook quickly in boiling, salted water for two to three minutes before carefully draining and refreshing in ice cold water. Drain and set aside.
To serve, remove the potatoes from the fridge and mix in the beans, olives, tuna, pepper, onion and half the parsley. Divide into bowls, top with the egg and remaining parsley and serve.