Put the garlic, lemon zest, capers, lemon juice, parsley and dill in a processor and whizz to make a coarse paste.
Rinse the vine leaves well and trim off the stems, then pat dry.
Lightly season fish with salt and pepper, and spread the pesto evenly over each piece. Place two vine leaves on a working surface and spread out each leaf flat – vein side uppermost. Place one piece of fish in the middle of the leaves. Fold up the bottom, then the side and finally fold down the top, ensuring that the fish is completely encased. You can secure the bundle with a toothpick if it's being stubborn!
Lightly brush with oil. Repeat with remaining fish pieces. Place in fridge until ready to cook.
Preheat grill or barbecue. Place fish packets over a medium high heat, you can use a fish or meat holder to make it easier to turn. Cook for about 4 minutes then gently turn. Continue cooking for 4 more minutes. Gently poke with a knife to check fish is cooked through. Remove from grill and serve.