I noticed this question posted by Black Elk in a couple of threads, so I sketched out the following answer which I’ll post in both threads.
I’d be in favour of using the term “Commonwealth” (“the Commonwealth”, “the Commonwealth nations”, etc.). For the period from the end of WWI to the end of WWII (thus in a time frame which works for A&A 1940), the term “Commonwealth” can be interpreted as referring more or less just to the six self-governing Dominions of Canada, Australia, New Zealand, South Africa, Eire (originally the Irish Free State) and Newfoundland (which, it should be noted, voluntarily agreed to go back to being ruled from London during the Great Depression).
The phrase “(British) Commonwealth of Nations” originated – at first with unofficial status – in the late 19th century, resurfaced (still unofficially) in 1917, and finally received official recognition in 1921. It was intended to be used in parallel with (or in some cases as an alternative to) the phrase “British Empire”, an example being Churchill’s famous statement that “if the British Empire and its Commonwealth last for a thousand years, men will still say: This was their finest hour.” The “Commonwealth” usage arose in recognition of the fact that a number of British territories had become self-governing – the first such case being Canada, the original “Dominion” – and that therefore they had a greater degree of sovereignty than the Britain’s colonies, protectorates and mandates.
Dominion status was granted to Canada in 1867, Australia in 1901, New Zealand in 1907, Newfoundland in 1907, South Africa in 1910 and the Irish Free State in 1922 (it became Eire in 1937). Via the Balfour Declaration of 1926 and the 1931 Statute of Westminster, it was recognized that these six Dominions were equal in status with the UK and that they were “freely associated as members of the British Commonwealth of Nations.” Strictly speaking, it could be argued that the UK was also an equal-status “member” of the Commonwealth rather than its head, but this would be a bit like arguing that the Augustus was basically an ordinary Roman Senator who simply happened to be “first among equals” in the Senate rather than the Emperor (an argument which Augustus himself liked to make). A similar dynamic existed within the Commonwealth by virtue of the fact that the UK’s (resident) Sovereign was recognized by the Dominions as their (absentee) Head of Statec – so Churchill’s phrase “the British Empire and its Commonwealth” is actually a good description of the asymmetrical relationship that existed at the time.
The phrase “Commonwealth” as it is used today has important differences with what it meant in 1940, since it now covers more than 50 entities. Back in the 1930s, it essentially referred just to Britain and its self-governing Dominions, of which there were six. The list started growing after WWII, when India, Pakistan and Ceylon were granted Dominion status, but the only British territories to achieve Dominion status prior to WWII were the six so-called “white colonies” whose population was preponderantly of European ancestry. So all in all, I think it’s historically justifiable to refer to the A&A 1940 “grey sculpt” block as simply “the Commonwealth,” which is certainly more convenient than the convoluted phrase “the self-governing Dominions of the British Commonwealth of Nations.” “The Commonwealth Dominions” (perhaps “the CDs” in shorthand?) would be my second choice: it’s longer than just “the Commonwealth” but it’s a trifle more accurate since it excludes the UK and thus refers only to Canada, Australia, New Zealand, South Africa, Eire and Newfoundland.