Look around. There are quite literally hundreds of posts here on Desi-Style or maybe "London-Style" kebab palaces. I do assume you refer more to the Pakistani/Indian style than "Middle-Eastern" or Turkish, given London's demo. But maybe not, since there seems to be a lot of doner type places also.
I wrote some stuff about the Original Kababish of London, a self-consciously Londoner Desi kebab place long ago. I like the keema nan, but there are better on the street.
For starters, you might search for the South Asian ilk: Khan, Kababish, Baba's, Hyderabad; for the more Middle-Eastern: Salam, Noon-O-Kebab, Steve's, Sahar. See also, posts re tacos al pastor. A South Asian/Arab hybrid is Kebab Corner, just outside the Loop. In Chicago, these places tend to be called "cabbie joints," for better or worse. Not nearly as Anglicized (ha) as what's in Lon.
The London kebab places even have legal counsel, apparently.