The vista after climbing to the roof of the dingy pub in the prologue implies it's somewhere in Southwark. Rather than being a rundown neo-Dickensian slum, it's one of the most multicultural, and more importantly most expensive, areas in London. The chances of finding a dive like that, which openly breaks the smoking ban too, are slim.
The abandoned section of the London Underground is a bit of a stretch too, since not only is the actual Tube network not that extensive south of the river, a lot of what's there is far more modern than as depicted (The Victoria and Jubilee line sections south of the river are both post-1950) and in extensive use. The closest part of the network to what is depicted would be the Aldwych branch, a complete section of tunnel closed in 1994, which is north of the river.