Late last night, on your behalf I searched all through the very long British Army Buttons webpage at the Colchester (England) Treasure Hunters website, and also through all 35 pages of British Military buttons at the UKDFD. I did not find a precise match for your button. But I did find that in the 20th-Century, a roman numeral was added in between the "GR" on some British Army buttons. I seem to see a "V" in between the GR on your button - which may mean it represent King George V, dating your button to 1940-48. The specific version of crown on it does indicate British Royal Army usage. There seems to be a fourth letter, which I cannot identify -- it might be a T or an L. So, I suspect your button is a "named regiment" British Commonwealth Army button. Because its backmark seems to be a New Zealand button-maker/dealer, perhaps your button represented a named regiment in the New Zealand or Australian army.