With a sharp knife, cut 6 deep slits into one side of each of the mackerel. Put in a shallow, non-metallic dish and brush all over with the oil.
Mix together the ginger, garlic, soy, parsley, honey and the lime juice and zest. Spread over the mackerel, pushing it into the slits. Cover with clingfilm, and marinate in the fridge for 20 minutes.
Meanwhile, combine the cucumber, dill and vinegar.
Cook the mackerel on the barbecue, or in a preheated griddle pan, for 5 minutes on each side until cooked. Sprinkle with paprika and serve with the cucumber salad and lime wedges.