I claim "The Big Smoke (or just "The Smoke") for London - it was so known during at least the late C19 - I'd have to trawl through some of my deeply buried notes, but I think I have a reference from the 1880s.

In the C18 and early C19, Cobbett, (that wonderfully irascible reporter who thought that potatoes were fit only for pigs and Irishmen - though perhaps a little too good for the latter!) invariably refered to Londonas "The Great Wen" - but that was before the Industrial Revoution had made London really smoky.

I have a feeling that Edinbuurgh had its soubriquet of "Auld Reekie" long before that - am I right, Jo? Maybe the inhabitants could afford bigger and better fires than the Londoners - or maybe it's because Edinburgh is a damned cold place!