alternatehistory.com

The challenge is for the UK Labour Party to undergo the same process of pasokification that affected many continental European socialist parties.

Specifically, change things so that Labour in the most recent election (2017, though ITTL the timing might be butterflied to a different year) gets under 20% of the popular vote and is widely viewed as either/ or politically irrelevant or lackies of the Tories. You can either have an alternative challenger to the Tories, or just fragment the British party system so that Labour still comes in second.
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