You Do Need power plug adapter while traveling from Anguilla to Greece.

Here is Why You Need An Adapter

The outlet and plug type used in Greece are C and F and in Anguilla are A and B. This is how they look like.

Anguilla

In Anguilla, outlets of type A and B are in use.

Type A

Type B

Greece

In Greece, outlets of type C and F are in use.

Type C

Type F