alternatehistory.com

The Strange Survival of Liberal England
1929-1931: Ramsay MacDonald (Labour)
def. 1929 (Liberal supply/confidence): Stanley Baldwin (Conservative), David Lloyd George (Liberal)
1931-1935: Ramsay MacDonald (National Labour)
def. 1931 (National Coalition including Conservative, National Liberals): Stanley Baldwin (Conservative), Arthur Henderson (Labour), David Lloyd George (Liberal), John Simon (National Liberal)
1935-1937: Stanley Baldwin (Conservative)
def. 1935 (National Coalition including National Liberal, National Labour): Ramsay Muir (Liberal), Herbert Morrison (Labour), Jonh Simon (National Liberal), James Maxton (Independent Labour), Ramsay MacDonald (National Labour), Oswald Mosley (NEW)
1937-1940: Neville Chamberlain (Conservative)
1940-1946: Archibald Sinclair (Liberal)
1940 wartime coalition arrangement including Conservative, Labour, National Liberal, National Labour
1943 wartime coalition arrangement including Conservative, Democrats, National Liberal
1946-1950: Herbert Morrison (Democrats)*
def. 1946 (Liberal coalition): Anthony Eden (Conservative), Bob Edwards (Labour), Archibald Sinclair (Liberal), James Henderson-Stewert (National Liberal)
1950-1951: Gladwyn Jebb (Liberal)
1951-1956: Anthony Eden (Conservative)
def. 1951: Harold Macmillan (Democrats), Gladwyn Jebb (Liberal), Bob Edwards (Labour)
1956-1962: Harold Macmillan (Liberal Democrats)
def. 1956: Anthony Eden (Conservative), Annie Maxton (Labour)
def. 1961: Anthony Nutting (Conservative), Annie Maxton (Labour)
1962-1966: Donald Wade (Liberal Democrats)
1966-19??: Julian Amery (Conservative)
def. 1966: Donald Wade (Liberal Democrats), Tony Cliff (Labour)

*Forced to resign over the Groundnut controversy.

Basically, DLG isn't ill during the National Government formation and it sort of spins off from that, with Labour tearing itself apart, Archi Sinclair replacing Churchill as the 'war Prime Minister', and Macmillan's fantasy of a 'Centre party' becoming reality.