alternatehistory.com

Based on my much earlier "In Unity Security" (and its American sequel) of which a more complete version can be found in my test thread (here) this is a list of British leaders in that chaotic and radically different universe! (Will answer questions, though it should mostly be self-explanatory)!

Prime Ministers of the United Kingdom;

1919-1922: Arthur Henderson (Labour)
1919: (Coalition with National) def - David Lloyd George (National Government), Sir Richard Cooper (National), H.H. Asquith (Liberal)
1922-1926: Austen Chamberlain (Centre)
1922: (Coalition with Liberals) def - Arthur Henderson (Labour), Sir Richard Cooper (National), Richard Haldane (Liberal), Noel Pemberton-Belling (Vigilante)
1924: STV Plebiscite: Yes
1926-1929: Ramsay MacDonald (Labour)
1926: (Popular Front Coalition with Liberals and Communists) def - George Curzon (National), Austen Chamberlain (Centre), Noel Pemberton-Billing (Vigilante), Reginald McKenna (Liberal), Albert Inkpin (Communist)
1929-1937: Henry Petty Fitzmaurice (Centre)
1929: (National Government with National, "Government" Labour and Liberals) def - James Maxton (Independent Labour-Communist Popular Front), William Joynson-Hicks (National), Oswald Mosley (Modernist), Phillip Snowden ("Government" Labour), Reginald McKenna (Liberal)
1933: (National Government with National, "Government" Labour and Liberals) def - Lewis Silkin (Independent Labour-Communist Popular Front), William Joynson-Hicks (National), Oswald Mosley (New), Phillip Snowden ("Government" Labour), Winston Churchill (Liberal)
1937-1937: James Maxton (Labour)
1937: (Popular Front Coalition with Communists and Continuity ILP) def - Oswald Mosley (New), Rowland Hunt (National), Rhys Hopkins Morris (Liberal), Malcolm MacDonald (Progressive), Neville Chamberlain (Centre)
1937-1938: Oswald Mosley (New)
1937: (Patriotic Front with National and Centre Backed by Military Forces) def - James Maxton (Labour-Communist-ILP Popular Front), T.S. Elliot (National), David Lloyd George (Progressive Liberal Alliance), Neville Chamberlain (Centre), Rhys Hopkins Morris (Continuity "Classical" Liberal)

First Minister of the Imperial Federation;

1938-1945: Oswald Mosley (New)
1938: National Ministerial Plebiscite: Yes
1943: National Ministerial Plebiscite: Yes
1945-1947: Harold Nicolson (New backed by Military/Industrialist Junta)

Prime Minister of the Union of Great Britain;

1947-1948: Dwight Eisenhower (Non-Partisan leading UN Military Transition)
1948-1958: Gwilym Lloyd-George (Progressive Conservative)
1948: (Majority) def - Ernest Bevin (SDP), John Simon (Democratic), Konni Zilliacus (Socialist)
1952: (Grand Coalition with SDP) def - Evan Durbin (SDP), Clement Davies (Democrats), Michael Foot (Socialist)
1956: (Coalition with the Democrats) def - Anthony Crosland (SDP), Michael Foot (Socialist), David Renton (Democrats), Hastings Russel (Social Credit)
1958-19---: Bob Boothby (Progressive Conservative-Democratic Coalition)