London is an old city; with many regions possessing identities of their own - because in centuries past, they were independent villages in the county of Middlesex. This has been a theme in novels of the twentieth century; notably, the G. K. Chesterton story The Napoleon of Notting Hill and Neil Gaiman's Neverwhere - even if the borough identities and histories of Chesterton are explicitly fabricated and although the attention of Neverwhere is not always on the character of the city, the boroughs have secret natures hidden in the cracks from those in London Above.
London has been brought low. Literally; the populace has retreated into the Underground, or has fled into the countryside. Sustaining such an existence is tricky; the Underground has little to offer in the way of arable land. Thus, those machines that can sustain some variety of life are jealously guarded. Some have managed to trade their way to prosperity, importing food to sustain themselves, wielding power over the poorer inhabitants of the tunnels.
These are the Great Companies; the Hammering Smiths, the Shepherds, the inheritors of whatever scraps of old world know-how they could claw together and pass on.
The Underground, in maps, is rather cheery and simple. Bright colours, simple lines - a complex network, to be sure, but a comprehensible one. The reality is different. This is not a system built for humans; it is one of tunnels lined with equipment and refuse, taking meandering, crooked routes. To be forced to live in these tunnels breeds a certain type of person, hardy and lean.
Hence, the dwellers of the new London -the fractious dwellers in the colour-coded tunnel-bands and the haughty, powerful Guilds.
At Best, these Guilds are Valiant Preservers of Old-World know-how, selling quality goods and services at a reasonable rate. At Worst, they are Monopolies with a chokehold on London, cloaked in tradition and secrecy.
At Best, the Colour Lines are full of hardy, plucky folk who have embodied a latter-day Blitz Spirit for longer than any might have imagined. At Worst, they are feckless tunnel dwellers who'll steal anything not nailed down.
Edit: a fairly scant section, I know. But I have a certain fondness for the main literary hooks in it; the Canticle for Liebowitz style religious (or pseudo-religious) orders preserving knowledge in a second Dark Age*.
The visual hook of the bright, smooth lines of the Underground map and the gloom of the tunnels is a good one. Even if the Tube map design dates from the 1930s, the contrast of the human-friendly face and intent of technology with the sordid reality is very Fallout. The cinematic application of this is obvious. Start zoomed in on bright well-lit tube map, whilst "We'll meet again" plays; drift back and out to show cramped tunnels and darkness, lit by gunfire.
*Possibly made darker "by the lights of a perverted science". Winston Spencer Churchill, 18th June 1940.