You Do Need power plug adapter while traveling from Saint Barthélemy to Northern Ireland.

Here is Why You Need An Adapter

The outlet and plug type used in Northern Ireland is G and in Saint Barthélemy are C and E. This is how they look like.

Saint Barthélemy

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

Type C

Type E

Northern Ireland

In Northern Ireland, outlets of type G are in use.

Type G