Boil the potatoes for 10-12 minutes until tender, adding the dwarf beans after 5 minutes and the runner beans for the last 3 minutes of cooking time. Drain and set aside.
Put the eggs into a small pan and just cover with water. Bring to the boil, then reduce the heat slightly and cook for 7 minutes. Drain and cool in cold water.
Put the tomatoes, anchovies, olives, chives and tuna in a bowl. Add the potatoes and beans and mix. Peel the eggs and cut into quarters, making sure they are cooked through. Arrange on top of the salad.
Whisk together the oil, pesto and lemon juice and pour over the salad to serve.