Comments on the British effort in Greece

 The idea that a Balkan Front could be established was simply a fantasy that had no real prospect of success. It was the sort of unrealistic thinking by Churchill that when Alan Brooke became the CIGS, he worked to squash, because that was a prime example of how Churchill would cause trouble. The British "moral obligation" to help Greece to fight the Germans was a real factor. During the British retreat in Greece, we saw that the Greek populace really appreciated the  British aid. 

The  British government had  a real concern about the American reaction if they ignored the plight of Greece in the face of a German attack. General Metaxas had opposed the British entry into Greece because he thought iy would weaken the British, which it did. General Metaxas died suddenly, and the new government welcomed British help. The Geek government wanted the British to wait to enter Greece until the Germans had moved into Bulgaria. The problem with that condition was that the British had little time to transport a force that was large enough to effectively oppose the Germans. 

The new Greek government understood the political importance for the British to help defend Greece against a German attack. The Allied side needed to see British soldiers fighting alongside Greek soldiers. Greek republicans accused Greek monarchists of being pro-German. When the British took a position at Thermopylae, "where Leonidas and his 300 Spartans fell", the British fought without any Greek help.

This is based om the account in "Greece, Crete, and Syria" by Gavin Long.