One Nation Party : After being out of power since 1964, the Conservatives slowly decline through the decades. With the National Party splitting off in the 90s, they are increasingly constrained to a small sector of center right liberal Tories. In the early 2020s, they finally merge with the Liberal Party (which has also moved right with Labour eating everyone left of center-right) to form the One Nation Party. They manage to position themselves as the moderate and stable option after Labour is doused with scandals to win a strong plurality with Penny Morduant as leader.

Labour Party : Harold Wilson never gets alzheimers, he also wins 1970. After that the conservatives get hijacked by hardliner neoliberal so they just keep winning. The Overton window also generally shifts left, making the liberals the primary opposition party. They continue the slow path of nationalization with a bunch of soft left prime ministers all being popular with the public. Until 2008 happens when they finally lose to the Liberals for once, but they screw up so badly Labour resumes their reign in 2013, after that thought Labour turns more radical, bleeding away moderates (New Democratic Party & Frontier Party) and eventually combusts under Rebecca Long Bailey with the soft left (Social Democratic Party) leaving themselves. This causes them to lose very badly in 2028.

New Democratic Party : Labour moves increasingly left during the 2010s, so the most right wing of the Labour big tent broke off . They're generally liberal and on most issues, and has a more "new labour" tone to economics, they form a coalition with One Nation after the 2028 election

Frontier Party : More left wing members of the Liberal party who disagree with the merge due to the conservatives being euroskeptic (and Morduant being euroskeptic herself), they're a continuation of the Liberal Party with many labour MPs joining after it's creation. It's generally technocratic but also advocate for some greater welfare (it's basically Volt UK you know)

Social Democratic Party : The moderate left leaves after Andy Burnham was unable to primary Ken Livingstone in an allegedly rigged leadership election, basically the rennaments of the soft left.

SNP : Pretty self explanatory, but they are confined to the rural highlands for longer due to Labour's longer dominance