Sheikh,
To be absolutely correct, I believe that what you refer to as British Isles is in fact the 'United Kingdom of Great Britain and Northern Ireland'. Great Britain refers to England, Scotland and Wales only. The full name of the UK has also been referred to as "The United Kingdom of Great Britain, Northern Ireland and Berwick-Upon-Tweed". Berwick-Upon-Tweed is a border town between England and Scotland and because its nationality was in dispute it was constitutionally enshrined as a separate entity.
Obs