Note: I am no historian, and wasnt educated in the UK, so I may make a few mistakes here and there. Whats here is based on my frequent tours of Museums, and what I can see on Google/Wikipedia.; Please correct anything you know is wrong.
First off, to folks who have never been to Britain (the UK). The UK was traditionaly made up of 4 countries, this is how it all came to be:
1: England - Despite what a lot of folk think, England is not the whole country. If you call it "England" when you're in one of the other countries, you can expect dirty looks at best, and a fight at worst (especially in the bad parts of Glesca).
2: Wales - Conquered/Annexed by the English in the 13th century, and merged into the English law system in the 16th century.
3: Scotland - Began sharing the same King with from James I (or VI depending on how you look at it) - The son of Mary Queen of Scots (who you've probably heard of) and succeeded Elizabeth I (who you've also probably heard of) because she didnt have any direct heirs(James was her Nephew) in 1603. However, they remained seperate countries (putting the king in an odd situation of almost going to war with himself - England's traditional enemy, France, was Scotland's tradional ally). "Great Britain" with Scotland and England retaining seperate legal systems, but a single government in London began in 1707.
4: Ireland - Similar situation, the crowns of Ireland and England were united (again, in a personal union, so the king was the king of more than one seperate country) in 1543 and an act of union came into being in 1800 again combining the Irish government with the British one (Becoming "The United Kingdom of Great Britain and Ireleand". This would remain the case (with a lot of dissent) until World War 1 where Southern Ireland (later the Irish Free state, and now the modern state of Ireland) managed to make "Home Rule" stick (so back to the many countries - One King thing... Which still goes on today with Canada, Australia, etc). Ireland remained Neutral in World War 2 (With many volunteers signing on with Britain anyway), and in 1949 becoming a fully independent republic. Northern Ireland at this point "opted out" of the Republic of Ireland, and remained in the Uk (or United Kingdom of Great Britain and Northern Ireland, as it says on my passport).
(Note, Cornwall is kinda funny, with some separatists claiming its a fifth country... but this isnt widely accepted...).
So thats history, and funny enough it just happens to end at Fallout's Divergence with the following as its probable status quo (based on the state of play in 1950)
The country is called "The United Kingdom of Great Britain and Northern Ireland".
Scotland retains a seperate Legal system, overseen by the "scottish office" (Uk Government Department), but no devolved parlement (in the real world, this would occur in the 1990's) - Westminster instead passes laws that essentialy have an English version, and a Scottish version, to keep everything level.
Northern Ireland with a devolved parlement (this would be suspended in 1972 in the real world), but a lot of internal fighting going on.
England and Wales as more or less one legal unit (in the real world, a limited devolved parlement would be setup in the 1990's for Wales)
The Dominions of the UK (Australia, Canada, NZ, etc) are more or less established as independent countries sharing the same Monarch - the only key differences is that we dont have Ambassidors between each other (an Ambassidor represents/stands in for the head of state, and having someone represent the Queen in a meeting with the Queen would effectively make put the Queen in a position of meeting herself - Back to the Future tells us this is a bad idea; Instead having "High Commisioners" take the same role), but still looking to the UK for guidance (kinda like Client states of an empire).
The UK has the strategic location of Gibraltar at the mouth of the Mediterainain (as it does today).
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Extrapolation of possible future - Feel free to debate any of this.
Groups like Plain Crymu (Wales) and the Scottish Nationalsist Party would be pushing for Devolution, or outright independence for their regions. However, this article http://en.wikipedia.org/wiki/Scottish_independence_movement#Scottish_home_rule suggests that scottish home rule didnt reinter mainstream politics until the 1960's.; Whilst the SNP was pushing for a system similar to today, it wasnt pushing all the way, and didnt win a parlementary seat until 1967.
If we accept that the world didnt move on much from 1950's thinking everywhere (not just in the US), then Scotland could reasonably be considered to have a devolved Parliament like today but All out independence is right out for scotland at least.
In Wales, this article http://en.wikipedia.org/wiki/Welsh_independence suggests Plaid Crymu started getting electoral success in 1960, suggesting a groundswell toward the end of the 50's, in turn suggesting a welsh independence movement in Fallout's world could have developed further than the scottish one - But not enough to secure it.
Northern Ireland more or less made its structual intentions clear in 1949.
So I would suggest that Wales and Scotland Devolved. Probably to the same timescale, and same rights and powers as the real world as this is a development of a movement that was clear in the 1950's, but they remained in the UK and there wasnt a question of them leaving. Northern Ireland too, but the sectarian violence probably continued (unlike thankfully in the real world).
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I know its a bit heavy, and there'll probably be some winges about me quoting wikipedia there, but does anyone have any comments?