Cook the rice in plenty of boiling water for 20–25 minutes, or until it is tender. (The grains will start to split open when they're just cooked.) Add the green beans and cook for 2 minutes.
Meanwhile, lay the mackerel on a foil-lined grill rack and brush with 1 tablespoon of the oil. Cook under a preheated grill for 8–10 minutes, or until cooked through. Leave to cool.
Drain the rice and beans and mix together in a salad bowl with the olives, anchovies, tomatoes and eggs. Flake the mackerel, discarding any stray bones, and add to the bowl.
Mix the remaining oil with the lemon juice, mustard, chives and a little salt and pepper, and add to the bowl. Toss the ingredients lightly together, cover and chill until ready to serve.