Trim excess fat from the meat and cut into walnut-sized pieces. Place in a bowl and add the thyme, garlic, lemon zest, 100ml (3½fl oz) of the olive oil, red wine and seasoning. Mix well and wrap the meat and flavourings tightly in clingfilm. Refrigerate, ideally overnight, for the meat to absorb all the flavours.
About half an hour before grilling, drain off the meat marinade juices and reserve. Preheat the barbecue or grill. In a small jar with a lid, combine the marinade juices with the lemon juice and remaining olive oil. Screw the lid on and shake until the dressing is amalgamated.
Thread the chunks of meat on to long skewers and brush with some of the dressing. Over hot coals, barbecue the souvlaki until they are done the way you like them. Remove the skewers from the barbecue and rest the meat in a bowl for 10 minutes. In the bottom of the bowl should be some delicious meat juices.
Brush the flat breads with the dressing, then dip them in the meat juices. Throw them on the hot barbecue and let them get some colour, but do not allow them to become crisp.
Arrange the meat on the flat bread, spread on some tzatziki and top with sliced tomatoes, pickled cucumber, and a sprinkle of sweet paprika. Roll the flat bread in a piece of parchment paper and serve.
Recipe from The Real Greek At Home, by Theodore Kyriakou & Charles Campion, published by Mitchell Beazley, £12·99.
See more Greek recipes
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home.