One scenario I've been thinking of for this is if Labour had been able to win a more workable majority in 1950 (say 20-30 seats). This would have two main consequences:
Firstly, Labour would be able to benefit from being in office during the postwar economic boom, which gives them a good position to win re-election in 55 and 60. In addition, remaining in office would go some way to alleviate the tensions between the left and right wings of the party whose internal disagreements were heavily informed by multiple election defeats IOTL, which means a more unified party.
Secondly, it gives the Liberals a chance to recover from their disastrous showing in 50 where they pulled out all the stops to contest as many seats as possible and ended up losing a quarter of their seats. IOTL this left them extremely weakened and in no position to fight the 1951 snap election which basically forced them to give up any pretensions of being a major party. Having a full 5 years to recover puts them in a stronger position to remain relevant and also means that they could serve as a spoiler for the Conservatives, further entrenching Labour's postwar position.
This puts the Conservatives in a difficult position. Repeated election defeats are going to exacerbate internal factional tensions as different groups keep pointing fingers and blaming each other for their exile to the political wilderness. Around the mid-50s, after the Tories lose their third election in a row, the National Liberals decide to end their association with the Conservatives and rejoin the Liberals, effectively doubling their seats. With Labour hegemonic, the Liberals on the rise and the Tories in disarray things come to ahead and the Tories split during the 60s SDP style with the modernising centrists going their own way. This gives the Liberals the chance to take the lead as leaders of the opposition. Afterwards they absorb the centrist offshoot of from the Conservative Party and go on to win the next election forming the first non-Labour government in about a quarter of a century, establishing a new two-party system and relegating the rump Conservatives to political irrelevancy (incidentally fulfilling Nye Bevan's dream of 25 years of Labour government and the political extinction of the Conservative Party).
hmm that's not quite correct, efforts were ongoing until 1922 and the famous meeting which Bonar-Law nearly did not attend, but in the end, did resulting in the overthrow of the coalition. It is fair to say Tory back benchers were no keener on merger than many Liberals.Lloyd George tried in 1919 to get the Coalition Liberals to merge with the Conservatives to form a "Centre Party." The decisive opposition to this plan came not from the Conservatives (who knew they would dominate the "new" party, whatever its name) but from the Coalition Liberals, who made it clear that they still regarded themselves as Liberals. Even if LG could have gotten more of the Coalition Liberals to go along, and such a party was formed, it would still be basically a Conservative party (especially since some Coalition Liberals were certain to refuse to join it) and would still eventually oust LG. Indeed, even if the "new" party included the word Liberal in its name, it would be no more "liberal" than the Australian Liberals today.
who is Alec Duncan-Smith? Douglas-Home? I cant see the Tories doing Vietnam, maybe they could dig in in 1951 in against Atlee and the Liberals over the welfare state and marginalise themselves, but Vietnam seems unlikely.In 1951 the Tories benefited from the absence of Liberal Challengers in many seats, and the underfinanced campaigns run by those that did compete. If the Liberals did slightly better in 1950, it could make the difference in some of the closest Labour-Liberal Seats. In this scenario there is unlikely to even be a snap election as with a larger Labour majority, Clemente Attlee will be less receptive to the argument over the kings health which would create a major complication if the government lost its majority or needed to call a snap election.
One answer could be if Alec Duncan Smith is able to pull out a very narrow victory in 1964 and promptly gets Britain involved in the Vietnam War. A more right wing Labour leader, such as James Callaghan who blamed Gaitskell's defeat in 1959 on his opposition to the Suez Canal Invasion, could lead to the Liberal party becoming the voice of educated liberal, middle class, and youth protest. With the Tory party loosing ground over the Vietnam War, it is possible they could split in government or fall in a vote of no-confidence. One outcome could be the emergence of Enoch Powell, who attempts to run on a right wing immigration platform (combined with admitting Vietnam was a mistake), or of another leader trying to appeal to traditional Labour supporters on a policy of immigration restrictions.
This could mean that politics is realigned as the Tories become an EU Skeptic, anti-immigration party, Labour as the left wing party and the Liberals as the party of the middle, often forming coalition with the left, or any other smaller nationalist, left wing or right wing party which emerges.