Since Fallout is a blend of retrofuturism and rule of cool, I have a few Anglocentric ideas.
Liverpool-Chester low level war: Seeing as Chester will probably avoid atomic attack and is surrounded by farm land, I can see it scraping by as a city-state, quite conservative place. Meanwhile you have an obliterated Liverpool up river, and playing on stereotypes (I'm a Scouser, there's whopping grains of truth) you could have it as a centre of ghoul activity and something of a trouble spot/hell zone, say ghoul raiders constantly attacking down the Mersey for supplies and zealous Cheshirites battling them to cleanse the region, however never meeting with success due to the sheer size of the task.
'Royal Navy' pirates: This is less plausible due to the resource problem but I like the idea of Navy ships surviving the bombings due to being out at sea and being used to raid the coastal settlements for resources, however I can imagine by the time of collapse most European ships being atomic powered so its a possibility. So you have descendents of seamen, whole clans aboard ancient, rusting battleships.
Coalpunk Mining Communes: From what I can gather from the backstory, the war for oil ended abrutly and led to near instant collapse of a petrol powered society. In such a sudden fall, I doubt there'd be much time to switch to coal or nuclear power. The idea of T'socialist republic of Yorkshire is intriguing but I think it would happen on a smaller scale. Say with former mining towns, shadows of their former self, turning to the old mines for energy. I can imagine a collectivist bent and maybe even the old Unions forming a basis for an organised society. They could be very insular settlements, 'neutral' possibly supplying other settlements. If you want to push the culture/political clash idea, they could have a strained relationship with the rump Royalist/Civil Servant underground government, constantly shifting between trade and war.
Blackpool Nightmare: Oh the possibilities! An English New Vegas but so much more. I'm thinking a cross between Bioshock and Reeves & Mortimer in terms of tone, a dark, utterly ridiculous Northern nightmare. Pompous local self-appointed Town Council maintaining a veneer of normality while ghouls prowl the streets, battling against machine gun toting Council Workers. Government organised by a casino-parliament with bets on new laws, leading to ever crazier laws as people attempt to win that deluxe seaside property they've always wanted. Could make its wealth as an entreport from relatively stable Ireland (what with Liverpool acting as a bottleneck on the Mersey), acting as a black market for strange weapons, supplies, slaves etc. Not to mention the seedier side of Blackpool could be turned up to 11, wierd mutant sex shows gladitorial seaside events, hosted by fat, raspy Lancashire comedians. Hell why not have Bullseye but with live targets. AND mutated feral seaside donkeys.
Mods, Rockers, Skins and Punks: Nothing too orginal but obviously the youth gangs of the period would be a possible source of power in devastated cities. Maybe Brighton is a somewhat functioning city state, with Mods and Rockers battling like Italian family clans for control? Naturally due to the fuel problem they'd have to ride bicycles, with crushed coke cans in the spokes. Could have intergang jousts on bikes? Actually...
Camelot!: Abandoned Arthurian theme park becomes home to a Himmler-style nutter who thinks he's King Arthur and gathers his knights, regularly jousting. Basically imagine Don Quioxte got a following and wore riot gear. Also the obvious Python reference if horses/bicycles are scarse.
*Vaults: Though no British vaults were created there were plenty of long-term underground shelters created for local bureaucrats and security personnel. I like the idea of some Civil Servants and families hiding underground, realising the above ground situation probably won't improve and carrying on as if everything is normal in the bunker, until madness ensures. Yes Minister guest written by Franz Kafka and Rod Serling.