You are correct (but not in your naming), so lets get pedantic: * Kingdom of Britain is 1707-1801 * The United Kingdom of Great Britain and Ireland 1801-1922 (official name change in 1927) * The United Kingdom of Great Britain and Northern Ireland 1922(27) - now Since this article quoted 1900, then you will find that the title I posted above is the correct one for the time frame.
In fairness theres a bit more to it than nomenclature I'm not sure its something you colonials would understand.