Which action prompted british prime minister winston churchill to declare that an iron curtain had fallen across europe?

Stalin's expansion into eastern European states. 

This was not a conquest but communist ideas were spreading with Stalin's encouragement. Countries in Eastern Europe began moving to communist countries. 

Stalin's move to surround the USSR with communist countries is the beginning of a sphere of influence. Churchill saw Great Britain on another side, one with the US in being democratic world powers. The speech stating there was an "iron curtain" reveals the split between the USSR and Great Britain and the US. 

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