You Do Need power plug adapter while traveling from Saint Barthélemy to Great Britain.

Here is Why You Need An Adapter

The outlet and plug type used in Great Britain 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

Great Britain

In Great Britain, outlets of type G are in use.

Type G