In this speech, Churchill is making an implicit comparison between communist governments and the Nazi party. Churchill gave this speech in March 1946. This was roughly six months after the end of World War II. Therefore, the Nazi party would have been very present in the minds of the listeners.
In the speech, Churchill refers to the communists parties as "raised to permanence and power beyond their numbers." This suggests that the people did not support the parties as much as the parties claimed. Moreover, he says that these parties want "totalitarian control," which implies a dictatorship. Both of these were significant characteristics of the Nazi Party.