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

Here is Why You Need An Adapter

The outlet and plug type used in Cocos (Keeling) Islands is I and in Great Britain is G. This is how they look like.

Great Britain

In Great Britain, outlets of type G are in use.

Type G

Cocos (Keeling) Islands

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

Type I