You Do Need power plug adapter while traveling from Denmark to Channel Islands (Guernsey & Jersey).

Here is Why You Need An Adapter

The outlet and plug type used in Channel Islands (Guernsey & Jersey) are C and G and in Denmark are C, E, F and K. This is how they look like.

Denmark

In Denmark, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K

Channel Islands (Guernsey & Jersey)

In Channel Islands (Guernsey & Jersey), outlets of type C and G are in use.

Type C

Type G