1937-1943 Winston Churchill
1943-1947 Lord Halifax
1947-1953 Horace Wilson
1953-1954 Montgomery
1954-1965 Clement Attlee
1965-1971 Harold Wilson
1971-1996 Margaret Thatcher
[1] At Britain's lowest point in the war, Churchill succumbs to a bout of pneumonia and is replaced by the respected Lord Halifax.
[2] Halifax oversees closer co-operation with the US and the dramatic invasion of Europe's "soft underbelly" in 1944. He serves until the end of the Second World War in 1945 but, tired of conflict and acutely aware of shifting public opinion, doesn't push the Soviets as hard on postwar jurisdiction Churchill did IOTL. While hardliners cry foul and much of Eastern Europe is swallowed by the Red Tide, the move is widely seen as a sensible effort to preserve peace and the Conservatives survive the 1945 election. Halifax retires from politics two years later to teach at Cambridge.
[3] Horace Wilson, a supporter of Chamberlain's appeasement, never expected to become Prime Minister. However Halifax's time in office has allowed the public to forgive and forget, and Wilson (who had spent the 40s on the sidelines) is seen as an easy way to prevent a leadership struggle. His initial term in office is successful but unexceptional. Following the 1951 election, a sharp post-war recession hits and riots and strikes sweep the nation.
[4] The "Cold Year" culminates in an attempted bombing of the House of Commons by pro-Soviet terrorists. In a
totally legal manoeuvre, respected war hero Bernard Montgomery is given a seat in the House of Lords and placed in charge of a "National Government". His harsh crackdown extends beyond radical groups to the left-most fringes of the Labour Party, and when police attempt to arrest several sitting Labour MPs the Queen forces him to call a general election.
[5] Labour, with Clement Atlee at the helm, is swept to power in a massive landslide. Atlee quickly institutes a radical program of nationalisation and sweeping welfare reforms, while Foreign Secretary Ernest Bevin organises Britain's allies into the "European Alliance" to combat the increasingly powerful communist bloc. Scholars usually mark this as the point where the UK replaced the increasingly-isolationist United States on the world stage. The Mandate of Palestine is split between Zionist and Arab spheres of influence. Atlee retires for health reasons in '65, passing the torch to his protege.
[6] Harold Wilson initially benefits from a booming economy and a period of relative national and international peace. However, he is soon forced to lead to EA on behalf of pro-Western forces in the Polish Civil War and is troubled by the rise of Irish nationalism. Then the unthinkable happens: an IRA cell attacks the Queen during a tour of Belfast, killing her. Wilson attempts to keep the country calm but is instead blamed for allowing the murder to happen and not pursuing those responsible. The 1971 election sees a very different Conservative Party return to power.
[7] The "Iron Lady" to her supporters, the "Witch" - or worse - to her many enemies. Margaret Thatcher sweeps into office and changes the country forever. Calling for an end to the post-war consensus and "total war" against the IRA, she massively enhances government power, turns Northern Ireland into a battleground, and openly challenges the decaying Soviet Union on the world stage. And, for the most part, it works. Sure, the "Troubles" are still ongoing (and most of Scotland is ready to declare independence at the drop of a hat), but the economy is chugging along and Britain is the undisputed master of the free world. For the Conservative Party, and the country they rule, the future looks bright.
Apologies for any egregious breaches of character, I'm not exactly an expert on British politics.