You'd need a bigger vacuum to the left of Labour. Perhaps the wartime coalition continues somehow, Labour go onto lose the next election after that, and someone like Gaitskell is more successful at getting reforms passed to Clause Four. As a result of Labours drift toward the Tories, ex ILP members are more likely to join the Communists than Labour, providing it with more support which is relatively moderate rather than Stalinist, and so it is quicker to reform itself toward Eurocommunism. They could later on build up support in Labour areas that are on the sharp end of deindustrialization, particularly if there is a moderate Labour government in place, and they could end up as a working class anti establishment option, as they have become in France, and right now, they could be riding the populist wave. Maybe a name change or an assocation with a larger left wing alliance might be needed, though, the term Communist is going to be toxic whilst the Cold War is happening, unless you get rid of that altogether, which I suppose is an option too.