We live in The United Kingdom of Great Britain and Northern Ireland, Northern Ireland isn't part of Great Britain.
Great Britain consists of 3 countries, England, Scotland and Wales.
The British Isles is a geographical location and not a political location and consist of most of the islands surrounding Great Britain including all of Ireland (Republic of Ireland and Northern Ireland) and the Orkney and Shetland Islands, the Isle of Man and many more.
The British Islands includes United Kingdom (England, Scotland, Wales and Northern Ireland), the Channel Islands and the Isle of Man.
There is no such thing as a British Passport, its a Passport of the United Kingdom of Great Britain and Northern Ireland.
As I said before Irvine isn't British.