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Bit of a Grauniad Lefty fantasy I know but what is the possibility of the conservatives being the party in decline instead of the Liberals and the majority of the 20th century being a back and forth between Labour and the Liberals? Probably with the Tories remaining a third party.
(Double points if you write a TL where the more conservative Liberals form an alliance with the Conservatives in the early 1980s before merging in 1988. Triple points 2011 has a Liberal-Conservative Coallition.)