Combine the lamb, onion, garlic, rosemary, anchovies and some salt and pepper in a bowl and use your hands to work them together. Divide into 12 and shape into even-sized, sausage-shaped patties. Chill for 30 minutes.
Thread the patties on to metal skewers, brush lightly with oil and barbecue for 3—4 minutes on each side until cooked through. Keep warm.
Meanwhile, make the salad. Combine the tomatoes, onion, olives and basil in a bowl and season with salt and pepper. Drizzle with oil and squeeze a little lemon juice over. Serve the kebabs with the salad.