Place steak in a large resealable food bag. Whisk olive oil, lemon juice, Worcestershire sauce, garlic, oregano, salt and black pepper in a small bowl. Reserve 125ml marinade for vegetables; pour remainder over steak and turn to coat. Seal bag. Chill at least 2 hours or up to 12 hours.
Preheat oven to 230 C / Gas 8. Line a baking tray with foil.
Toss chickpeas, tomatoes, cucumber and red onion with reserved 125ml marinade on the prepared baking tray and spread in an even layer.
Roast on centre rack until vegetables begin to brown, 15 to 20 minutes.
Remove baking tray from oven and turn on grill. Push vegetables to the middle of the pan. Remove steak from marinade, allowing excess liquid to drip off, brush off garlic, and set on top of vegetables. Discard marinade.
Grill steak on top rack, flipping once, until it begins to get charred, 3 to 5 minutes per side for medium-rare.
Turn oven off and place tortillas on the bottom rack of the oven; keep in oven until warmed and slightly toasted, 1 to 2 minutes.
Cover steak loosely with foil and let rest 10 minutes before slicing thinly across the grain. Fill tortillas with warm steak and vegetables; top with feta cheese and parsley.