In a large bowl, mix the oil, oregano, mint and lemon juice.
Cut the halloumi and vegetables into large chunks and add to the bowl of marinade, then toss to coat. Allow to marinade while the barbecue or griddle pan heats.
Thread the haloumi and vegetables onto skewers, then grill until lightly charred. Baste with any remaining marinade.
For the tzatziki
Cut the unpeeled cucumber lengthways and use a teaspoon to scoop out and discard the watery seeds. Chop the cucumber into chunks and pulse in a food processor a few times until it is finely grated. Place into a clean tea towel and squeeze out excess moisture.
In a bowl, mix together the cucumber, yogurt, lemon juice, vinegar, garlic, salt and pepper. Keep in the fridge until ready to use.
Lay out the flatbreads of wraps (warm first if desired). Unthread the souvlaki skewers and divide the halloumi and veggies between the wraps, drizzle with tzatziki and serve.