alternatehistory.com

1908-1914: Herbert Asquith (Liberal Minority with IPP Confidence and Supply)
1910 def - Arthur Balfour (Conservative/Liberal Unionist), John Redmond (IPP), George Nicoll Barnes (Labour)
1910 def - Arthur Balfour (Conservative/Liberal Unionist), John Redmond (IPP), George Nicoll Barnes (Labour)
1914-1920: Arthur Balfour (Unionist Majority)
1914 def - Herbert Asquith (Liberal), John Redmond (IPP), Eamon De Valera (Sinn Fein), George Nicoll Barnes (Labour)
1918 def - David Lloyd George (Liberal), J.R. Clynes (Labour), Eamon De Valera (Sinn Fein), John Redmond (IPP)
1920-1923: Walter Long (Unionist Majority)
1923-1925: Richard Haldane (Liberal Minority with Labour and IPCP Confidence and Supply)
1923 def - Walter Long (Unionist), Eamon De Valera (Sinn Fein), Ramsay MacDonald (Labour), John Redmond (Irish Parliamentary and Constitutional Party), Joseph Delvin (Irish Parliamentary and National Party)
1925-1927: George Curzon (Unionist Majority)
1925 def - Richard Haldane (Liberal), Arthur Henderson (Labour), Eamon De Valera/John Delvin (Irish National United Front), John Dillon (Irish Constitutionalist)
1927-1928: George Curzon (Unionist leading National Emergency Government with Liberals, Labour and Irish Constitutionalists)
1928-1929: Austen Chamberlain ("White Feather" Unionist leading "Peace" Government with Liberals and Labour)
1929-1934: Donald Maclean (Liberal-Labour Coalition)
1929 def - Sir Richard Cooper ("Martian" Unionists), James Maxton (Labour), Austen Chamberlain (Peace Coupon), Edward Carson (Irish Unionist), John Simon ("Martian" Liberal)
1934-1936: Samuel Hoare (Unionist-National Unionist Coalition)
1934 def - Oswald Mosley (Labour), Winston Churchill (National Unionist), Donald Maclean ("Official" Liberal), David Lloyd George (Independent Liberal), Philip Noel-Baker (Peace)
1936-1940: Samuel Hoare ("Government" Unionist leading National Government with Labour, Liberals and Peace)
1940-1941: Raymond Asquith (Liberal leading National Government with Labour, "Government" Unionists and Peace)
1941-1946: Leo Amery (Unionist Majority)
1941 def - Raymond Asquith (Liberal), Oliver Baldwin (Labour), Oswald Mosley (National Labour), Duff Cooper ("Government" Unionist), Philip Noel-Baker (Peace)
1946-0000: Leslie Hore-Belisa (Liberal-Centre Minority Coalition with Labour Confidence and Supply)
1946 def - Leo Amery (Unionist), Oliver Baldwin (Labour), Duff Cooper (Centre)

It's a no WW1 world! What happens here is that the Liberals, not tainted by WW1 (a version of which sees Germany beaten down quickly by Britain and France in 1915) don't die out and surge far longer. The Cinservaivea quickly become a semi-dominant party, with the Liberals and Labour both only ever big enough to form a government with one another's support. The Tories are only unable to become totally dominant because their vote is split itself, first in the 20s over the Irish Civil War and the "Ulster Question" (with the mainstream Unionist party unwilling to support Protestant Ethnic cleansing in the province) and then over the formation of a National Government to handle an alternate Great Depression in the late 1930s. Labour also splits over the issue of nationalism vs internationalism, with Mosley advocating a more imperialistic socialism which splits the party in two and prolongs the life of the Liberal Party. By 1946 the Liberals are, finally, on their last legs and are set to be overtaken by Labour, although they are so entrenched that they are almost certain to survive at a seat count just below Labour well into the 1960s...