To clarify: at no point was Harry Pollitt thown out of the CPGB. He was it's General Secretary from the late 1920s till the early 1950s EXCEPT for a short period at the beginning of WW2. At the start of the war the position of the CPGB was that the war followed the pattern of the Spanish Civil War ie was a war against Fascism and to be supported. Then the USSR signed the Ribbentrop Pact with Germany. A meeting was held of the Third International to which all major Communist parties were affiliated and voted to change the line to the same which many on the Left had held of the First World War, namely that it was an Imperialist war with each side as bad as the other. Dave Springhall, the British representative on the International returned and told the CPGB of the vote taken. The majority of the Central Committee agreed to change the line to that of the International. Pollitt, along with the Communist MP Willie Gallagher and Johnny Campbell of the Daily Worker argued against. Pollitt and Gallagher voted againt the final resolution (although they persuaded Campbell not to) and Pollitt was voted out of the position as Secretary to be replaced by Rajani Palme Dutt. Pollitt since he was no longer a Party official went back to working as a boiler-maker, but he remained in the Party. In about a year Germany attacked the USSR, the line of the International changed back and Pollitt returned to being Secretary. In the early 50s he became ill and retired, being given the position of Chairman.
The song (in case you thought I had completely forgotten about it!) however has absolutely nothing to do with the events described, since they were written in 1935 by a woman communist (teacher I think) called Elin Williams. Thje last I heard she was still alive though into her 90s.