Preheat a grill to a medium-high heat.
Fillet the mackerel and remove all the rib bones. You can ask your fishmonger to do this for you.
Season the mackerel well, squeeze a few drops of lemon juice and a sprinkling of zest over each fillet, and drizzle them with olive oil.
Place under the grill, skin side up, for five minutes. After five minutes turn them over to brown the meat which will be nearly cooked by now and should only need a minute or two. Set aside to rest.
To make the salad, boil the potatoes until firm but cooked, and cut them in half. Put them in a mixing bowl with a splash of olive oil, the rest of the lemon juice and zest, and the mustard and vinegar.
Mix together well, then add the finely sliced onion and fennel. Add a good amount of the parsley and season well.
Divide the salad between four serving plates to form a mound. Lay the mackerel fillets on top, and pour over the juices from the fish and the bottom of the salad bowl.