Cook the potatoes in a saucepan of lightly salted boiling water for 12–15 minutes until just tender. Drain and cool under cold running water. Meanwhile, gently lower the eggs into a saucepan of boiling water and cook for 8 minutes. Drain and cool as before, then shell. Cook the beans in a saucepan of salted boiling water for 5 minutes until just tender. Drain and cool as before.
Meanwhile, mix together all the ingredients for the vinaigrette and season well. Toss half the vinaigrette with the potatoes and beans and set aside. Rub the oil over the tuna and season well. Heat a griddle pan until smoking hot and cook for 2 minutes on each side until browned but still rare inside. Cut into bite-sized pieces.
Toss the tomatoes with the potatoes and beans. Separate the leaves of the lettuces, then arrange on a serving plate with the anchovies, olives, eggs, quartered, the tuna slices and drizzle over the remaining dressing.