You Do Need power plug adapter while traveling from Wales to Bhutan.

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G and in Wales is G. This is how they look like.

Wales

In Wales, outlets of type G are in use.

Type G

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G