A little point here.
Unless I have been mistaken for many a year, great(er) Britain was so called to differentiate the off-shore islands from the European Brittany .
Originally, it was a geographical reference so the correct term would have been great Britain. But over time the term was adapted as the name of the countries (England, Wales, Scotland and Ireland plus Cornwall, the Isle of Man and the Channel Islands) then the correct form would have been modified to Great Britain. [GB]
That general usage has given way to the defined new name of The United Kingdom of Great Britain and Northern Island which identified Great Britain as the mainland and not the other lesser islands.
Thus it was correct to refer to Northern Ireland with capitals but (say) south Wales or northern England in mixed cases.
As the Great Britain has evolved into the current United Kingdom [UK] the usage of the term Great Britain has become problematical inasmuch as people are unsure whether the great is still the geographical reference or Great being the correct country name.
Of course, we are still the 'United Kingdom of Great Britain and Northern Ireland' so the user of the lower case 'g' should be dragged outside and shot.
But he was probably Polish anyway...