Create a Britain controlled by a government similar to Stalin's Russia of OTL.
This is a different mission to the question in the thread's title. The Soviet Union had features of government specific to a general revolution kicked off in an Orthodox society with a large peasantry, by a working class, finalised by Bolshevist-style social democrats, and turned towards a brutal centrist opportunism by Stalin and similar opportunists in a context of working class demands increasing in the late 1920s. Providing these conditions for the United Kingdom is not going to happen without a PoD prior to 1400 in relation to the peasantry, and much earlier in relation to the nature of the peasantry and British christianity.
Providing the United Kingdom with a Stalinist government is a different matter, as we can do so through the CPGB—though any attempt will involve radical problems not faced by the United Kingdom historically.
I know that Britain is praised for have social reforms throughout it’s history so perhaps have a situation in Britain similar to Russia of OTL in which a government body becomes popular with the promise of equality for the masses and a leader of that body is elected head of the government but uses the position to usurp all of the states powers for there self.
Generally, analyses of the United Kingdom in the 19th century point to its retrograde social policies, including the continuous extension of the corn laws, the militant anti-franchise position of its ruling class, and the late, voluntary and half-hearted social insurance and trade union legalisation efforts.
This may require a pre-1900 POD so I will allow those. I have just one stipulation and that is that Winston Churchill is not involved in your TL for whatever reason.
Pre-1900 PoDs eliminate "Stalinism" as we know it, pre-1900 PoDs producing a Vozhd in the United Kingdom eliminate the United Kingdom, England, The Church of England (even if Catholic) and capitalism as we know it. Probably also "Europe."
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The simplest way to get a Stalinist government in the United Kingdom is an indefinite extension of post-war Tory rule under a war economy with maintained levels of conscription. Say another Indian Mutiny supplied by the Soviet Union while interventions in Greece expand with a complete contraction of US aid and credit; the RAF workers councils get shot, legitimising the CPGB military sections, and legitimising the CPGB's harder line with the left of labour. The attendant massacres during the General Strike of ?[1945–49, pick a year] further legitimise the CPGB and delegitimise the Labour Party with the working class. Mutiny in the RAF and RN result in the forcible demobilisation, and the return of the Military Committees to a Britain where significant portions of the United Kingdom are held by vaguely CPGB aligned Workers Committees.
This is very different to your desire, but it is vaguely realistic if the Tory Party lose their heads to cretinism. It also requires a call and response process of increasing RN/RAF/Army committee militance, a major civil war inside the Empire, and the Labour Party to lose public credibility due to massacres of workers in the UK.
yours,
Sam R.