Wash the courgettes and slice into ribbons, using a peeler. Set aside in a salad bowl.
Mix half the lime zest with all the lime juice in a small bowl. Stir in the Mint, drizzle in the olive oil and season to taste. Add the courgettes ribbons and toss to coat evenly.
Place the courgette ribbons onto individual plates or bowls. Flake the mackerel and add to the courgettes. Place 2-3 anchovy fillets on each salad, according to preference.
Drizzle with any remaining lime dressing and garnish with the remaining lime zest.