But his Irish history is a little off. Ireland was not a British colony in 1911, but an integral part of the United Kingdom, no different, at least in principle, than Scotland or Wales. Nor did it become fully independent in 1922. Instead it achieved dominion status, fully self-governing but with King George V as head of state and members of the new Irish Parliament were required to swear allegiance to him. In 1927, George V was formally invested with the title of King of Ireland, last held by George III before the Act of Union of 1801. So at this point Ireland’s status was the same as the other self-governing dominions of the British Empire, such as Canada and Australia. It was only in 1949, when the Irish Parliament passed the Republic of Ireland Act and the Parliament at Westminster passed the Ireland Act that stated that “the Republic of Ireland had ceased to be part of His Majesty’s dominions” that Ireland became fully independent.
At that time any member of the British Commonwealth which became a republic automatically ceased to be a member but could reapply, as India did when it became a republic in 1950 (it had been independent since 1947). Ireland chose not to reapply. Thus the first country to sever all ties to the British Crown since the Treaty of Paris acknowledged American independence in 1783 (not 1782) was actually Burma, which became independent and left the Commonwealth in 1948.
It is, I think, a testament to the British “fair play,” that Max refers to that so few countries have severed all ties to the British Crown. Besides Ireland, Burma, and the United States, I believe only Zimbabwe (likely to be readmitted once a democratic government is reestablished) and Hong Kong (which probably had no choice in the matter) make the list. Indeed one country, Mozambique, which was never a British possession, joined the Commonwealth in 1995.