Mix together the oil, paprika and cayenne with a little salt and pepper. Make 3 shallow cuts in the skin of the mackerel and brush over the spiced oil.
Place the lime quarters and mackerel on a hot barbecue, skin-side down first, and cook for 4–5 minutes until the skin is crispy and the limes are charred. Turn the fish over and cook for a further minute on the other side. Serve with a rocket salad.