Would A hugely Successful UK Communist Party Post WW2 Have been possible?

Actually even before WW2. We certainly had reasonably successful ones in France and Italy, so why not The UK, yes there was an established strong Labour party, but there were socialist parties in France and Italy side by side with quite strong Marxist ones! Also can you have a successful Militant-Trotskyist type Marxist party in the UK instead of a Stallinist one?
 
First past the post.

At it's height the Stalinist CPGB could only hold down one constituency at a time, running against Labour simply wasn't practical. However, they were a significant force in within the Unions and in leftist Social Movements.

Best you can hope for is a stronger and longer lasting Independent Labour Party, with Marxist backing.
 
Under a proportional representation voting system, especially like the one the Brits imposed on the ROI and originally the Statelette of Northern Ireland under the Anglo-Irish treaty, the British Communist party would have won quite a few seats in Westminister, possibly becomming the fourth party, The Liberals in their various guises would of course have a substantially higher seat representation than OTL also. But would there be massive frictions between Stallinists and Trots and who would win?
 
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