You Do Need power plug adapter while traveling from Luxembourg 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 Luxembourg are C and F. This is how they look like.

Luxembourg

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

Type C

Type F

British Virgin Islands

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

Type A

Type B