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

Here is Why You Need An Adapter

The outlet and plug type used in Anguilla are A and B and in Vanuatu is I. This is how they look like.

Vanuatu

In Vanuatu, outlets of type I are in use.

Type I

Anguilla

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

Type A

Type B