You Do Need power plug adapter while traveling from Cocos (Keeling) Islands to British Virgin Islands.

Here is Why You Need An Adapter

The outlet and plug type used in British Virgin Islands are A and B and in Cocos (Keeling) Islands is I. This is how they look like.

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I

British Virgin Islands

In British Virgin Islands, outlets of type A and B are in use.

Type A

Type B