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

Here is Why You Need An Adapter

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

Channel Islands (Guernsey & Jersey)

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

Type C

Type G

Réunion

In Réunion, outlets of type C and E are in use.

Type C

Type E