alternatehistory.com

Here's a Prime Ministers list for my TLIAW which I actually did in a week if you don't count the postscript.

1900-1903: Henry Campbell-Bannerman (Liberal)
1900 (Minority with IPP and Labour supply and confidence) def. Robert Gascoyne-Cecil, 4th Marquess of Salisbury (Unionist Pact --- Conservative / Liberal Unionist), John Redmond (Irish Parliamentary Party), Keir Hardie (Labour)
1903-1904: H.H. Asquith (Liberal minority)
1904-1909: Arthur Balfour (Conservative)
1905 (Unionist Pact with Liberal Unionists) def. David Lloyd George (Liberal), John Redmond (Irish Parliamentary Party), Keir Hardie (Labour)
1909-1910: Arthur Balfour (Conservative leading War Government)
1910-1914: Andrew Bonar Law (Conservative leading War Government with Liberals, Labour and IPP)
1914-1915: Ramsay MacDonald (Labour)
1914 (Minority) def. Andrew Bonar Law (Victory Coupon --- Coupon Conservatives / Coupon Liberals / IPP), Eamon de Valera (Sinn Fein), Henry Page Croft (Independent Conservative), H.H. Asquith (Independent Liberal), George Nicoll Barnes (National Democrat)
1915-1919: Andrew Bonar Law (Conservative)
1916 (Coalition with Liberals) def. Ramsay MacDonald (Labour), David Lloyd George (Liberal), John Hancock (Liberal and National Democrat)
1919-1922: Stanley Baldwin (Conservative minority)
1922-1925: Winston Churchill (Conservative)
1922 (Majority) def. J.R. Clynes (Labour), David Lloyd George (Liberal)
1925-1927: Stanley Baldwin (Conservative minority)
1927-1928: Stanley Baldwin (National Conservative)
1927 (National Government with Labour and Liberals) def. Ramsay MacDonald (Labour), Austen Chamberlain (Conservative), David Lloyd George (Liberal), Tudor Rees (Independent Liberal)
1928-1935: Ramsay MacDonald (Labour)
1931 (National Government with National Liberals and National Conservatives) def. Austen Chamberlain (United Front --- Conservative / Liberal / Independent Liberal), John Hancock (National Liberal), Stanley Baldwin (National Conservative)
1935-1938: David Lloyd George (Centre)
1935 (Coalition with ISL) def. Ernest Bevin (National Coupon --- Labour / National Liberal / National Conservative), Arnold Leese (Imperial Synarchic League), Harry Pollitt (Communist)
1938-1939: Neville Chamberlain (Centre minority)
1939-1943: Neville Chamberlain (Centre leading War Government with Labour, National Liberals, and National Conservatives)
1943-1948: Anthony Eden (Centre)
1943 (Majority) def. Herbert Morrison (Labour), Richard Acland (National Liberal), Harry Pollitt (Communist)
1948-1953: Malcolm MacDonald (Labour)
1948 (Peoples' Pact with National Liberals) def. Anthony Eden (Centre), Richard Acland (National Liberal), Harry Pollitt (Communist)
1953-1961: Rab Butler (Centre)
1953 (Majority) def. Malcolm MacDonald (Labour), Harry Pollitt (Communist), Donald Johnson ('Continuity' National Liberal)
1957 (Majority) def. Douglas Jay (Labour), Andrew Healey (Communist), Donald Johnson (Radical-Liberal)
1961-1966: Benjamin Thorneycroft (Centre)
1961 (Majority) def. Douglas Jay (Labour), Andrew Healey (Communist), Donald Johnson (Radical-Liberal)
1966-1969: George Maudling (Labour)
1966 (Majority) def. Benjamin Thorneycroft (Centre), Andrew Healey (Communist), Arthur Margolis (Radical-Liberal)
1969-1971: Leonard Callaghan (Labour majority)

Here's a link to the TLIAW