Well, I did write a huge wall of text describing the strange idea for London in response to Thande's post, and then my computer decided to BSoD on me. I'll try again (though I doubt it will be any shorter than it was before - I have a problem with brevity).
The Royal Family are evacuated to Hawthorn (also known as Turnstile, and about fifty other things) along with the Cabinet, PM, military commanders and about 4,000 staff before the war. They try to establish continuity of governance after the nuclear war, but damage to infrastructure means they can't establish direct authority beyond their immediate vicinity. The Regional Government Head Quarters (RGHQs) they set up to administer various parts of the country in their stead prove ineffective due to a number of reasons (e.g. being hit by a nuclear explosion, being unfinished, being understaffed, the relevant staff not evacuating to the RGHQ bunkers when the siren sounded due to the "cry wolf" effect, damage to infrastructure, opposition from the locals, and so forth), so no continuity of government is established beyond Wiltshire and the surrounding area.
Now, in London some government staff would have taken cover in the citadels under the city, but many don't survive the initial nuclear barrage. A significant portion of Londoners survive in makeshift and Civil Defence bunkers, but these bunkers are of poor quality, and so many Londoners become Ghouls.
With the British government (henceforth referred to as the Wiltshire government) stuck in Wiltshire, London's RGHQ (
Kelvedon Hatch) ineffective, and few surviving government officials in London, London is without an official government. Instead of breaking off on their own, they evolve into a semi-anarchic society, where various voluntary organisations (some formalised, others informal and ad hoc) maintain the society and the city they live in. At first they believe this is a temporary state of affairs whilst they wait for the Wiltshire government to organise itself and reincorporate London. Many Londoners listen to radio transmissions from the Wiltshire government, assuring them that they're coming and keeping them abreast of new developments. These messages also implore Britons to stay vigilant in the fact of the horrifying mutants that roam the land - most Londoners assume they mean the mutant dogs, foxes, etc., but some theorise they're referring to the Ghouls, who have become respected and knowledgeable members of London society.
When the Wiltshire government gets round to properly contacting London, many Londoners are hostile as they feel that they were betrayed by the government, who fled London leaving them to fend for themselves. They're not actively hostile, though, and they show no hostility in their initial meetings with the Wiltshire authorities beyond "Well you took your bloody time!". However, the Wiltshire government reveals that they do indeed mean the Ghouls when referring to "horrifying mutants", this offends the many well respected Ghouls in London society, and turns many Londoners against the Wiltshire government.
Unable to negotiate the peaceful incorporation of London, the Wiltshire government invades, believing that the Londoners would willingly accept them and it was only their leaders who were hostile. This proves incorrect, and the Londoners utilise their knowledge of the London subterranean structures to conduct a guerilla campaign against the invading Wiltshire forces. This campaign is successful, and the Wiltshire government withdraws, promising not to set foot in the Greater London area unless the people of London wish it so.
The current state of London is called the "London Anarchy" (though many Londoners prefer the "London Freedom", due to the fact that anarchy is usually incorrectly used to indicate lawlessness and savagery). There is no official or centralised government authority, but a series of co-operating voluntary organisations that maintain society. The most powerful of these are the Police/Civil Defence authority, who maintain order; the guild of merchants that trade on the Londoners' behalf; and an organisation whose sole role is to deal with governments from outside London (mainly Wiltshire), who're mainly concerned with the setting up of trade posts and the regulation of movement of foreign government/military officials. The government agencies that survived in London have kept their names, but have become caretakers who maintain government buildings, as well as vast repositories of knowledge and technology (sort of like the Brotherhood of Steel, but different due to having evolved out of a bureaucracy instead of a military).
Londoners mainly live in the network of tunnels and buildings under London, but many of them also live above ground, generally in small communities around the entrances to the underground.
I've also thought I should do something with Britain's more famous ports. Portsmouth would probably be absorbed into the Wiltshire government, and I've no idea what to do with Liverpool (or Manchester, or Birmingham, or that whole region), but I had an idea for what to do with Scapa Flow. Fallout canon states that the world's oil dried up some time before the war, so presumably Britain would have to either scrap or convert its oil-powered navy. I was thinking that some or all of the obsolete ships could be anchored in Scapa Flow whilst they await renovation or scrapping, with a large number of them still being there when the war broke out. After the war, the people of Orkney would start trying to salvage anything useful from the ships, before some of the decided that it might actually be easier to just live on the ships themselves. Over time the anchored ships would be moved close together and attached to one another. Structures would be built on their decks, and they would be connected to the mainland by rope bridges and gangplanks, resulting in a floating city sitting in Scapa Flow.
I'm still not sure what to do with most of the Midlands, though.