Well - does it? Britain's nickname is 'Old Blighty', so we're OK there, but what about the capital?
This forum seem to agree that 'The Smoke' is one... but surely that can apply to any number of cities (I'm sure I've heard it in numerous American films), so that doesn't work.
This site seems to think 'The City' and 'The square mile' count, but, although they stick to the rules of nicknames (one is a shortening, the other a physical feature), I still think they are a poor showing.
But hey - look at this (taken from here):
"The Big Smoke" (or, "the Great Smoke") is London, England -- a city known for its fog. "The Big Smoke" dates earlier than "the Big Apple," but London's nickname is used informally and much less often.The trouble is, there are so many Australians in London these days that use of Big Smoke may well be on the increase, but not in the right sense to make it a proper nickname. Our (admittedly already obscure and anachronistic) sense of national capital jocularity is being diluted by outsiders. Damn cheek. Just coz they don't have any city nicknames of their own. (Quite odd really, given the Australian propensity for nicknaming things. If I'm wrong, and there are nicknames for Australian cities, please correct me).
(Oxford English Dictionary)
the (big, great) smoke, a colloquial name for London. Also, any large city or town (chiefly Austral.).
Next they'll be importing a non-standard use of the term cockney -chuck another cockney on the barbie, or summat - and ruining that too. We should search Australians for vocabulary when they arrive in the same way they search us for animals and plants.