Man oh man... delicious...
The skewered stuff generally done on the grill is usually called shish, originated from the Turks. It's big across the Arab world, 'Shish Taouk', pretty much excellent clean street food grilled chicken pieces, with alot of great garlic sauce called 'Toum'. Plenty of Lebanese/middle-eastern restaurants in London do this, all over Edgware Road. Then you have the chicken/lamb shawarmas, lots of chilli and garlic sauce. Place called Taza on Queensway, London, does some messy, greasy, but saucy, really well done shawarmas that are making me fucking drool thinking about it.
Persian cuisine using the similar grill, but different marinades, you have the joojeh chicken kebabs, or koobideh (minced meat lamb/beef) - usually served with lots of rice, grilled tomato and some butter.
This hits the spot every fucking time. Good place called ALounak, in central London, near Bayswater. Great Persian food.
The Turks are really the best though, they do the shish, doner kebabs, grilled meats on their special charcoal grills. Stoke Newington, and Dalston - good Turkish areas on the outskirts of London, you'll find tremendous places.
London is full of kebab shops, all of differing quality, but there's always some place local, always close to a pub or bar.