In a large shallow container or bowl, combine the olive oil, lemon juice and zest, Worcestershire sauce, 1 tablespoon parsley, thyme and salt and pepper on both sides. Season with salt and pepper. Add the fish and turn to coat with the marinade. Cover and refrigerate for about 2 hours, but not more than 6.
Heat the grill to high. Carefully oil the grill grates. Remove the fish from the marinade and pat dry. Discard the leftover marinade.
Grill the swordfish for a total of 8 to 10 minutes, until the fish is just cooked though, turning it at least once during cooking. For more dramatic cross hatch marks, you can turn it (rotating the fish a quarter turn every time you slip it), a total of three times. When the fish it done, it should separate into flaky chunks when pressed.
Serve hot, sprinkled with the remaining parsley, with lemon wedges on the side.