I felt this correction was necessary because you made it sound like the people of Greece were fanatically anti-communists which was generally not the case.
Yes you are correct, The Greeks were not originally fanatically anticommunist, but a lot of them became so after the civil war when they saw all the atrocities committed by the communists in order to establish a Stalinist regime in Greece.
In fact more people were killed during the Civil/guerrilla war, than what they did from the Germans during the occupation.
The British had their own interests in Greece for their involvement, they wanted to dominate in the Mediterranean sea like they were even before WWII.This is just one more case of Britain's involvement causing more bloodshed than necessary.
Churchill and Stalin had agreed at Yalta, that Greece would fall under the influence of Great Britain after the war, unlike Bulgaria, Albania, Yugoslavia and the rest of the East European countries that were to fall under the influence of the Soviet Union.
Unfortunately for the British, three years later in 1947 they realized that they were not the great imperial power they used to be before WWII, and they couldn't afford to do the things they used to.
It was time for the Americans to take over!