Although WWI was extremely costly to the British Empire and all other participants in the war, the Empire actually had splendid prospects in the interwar years. Of course not in unchanged colonial form, but as a closely knit together commonwealth co-operating in economical, political and military matters. The transformation process was well underway in the interwar years, but basically WWII, where GB ended up totally clapped-out, made a commonwealth superfluous as anything but a social activity.
With no blood draining world wars at all, everything of course would have been very different, but I think a PoD could be as late as May 1940. In short, if the German campaign vs. France fails (not difficult to find plausible PoDs for that) the Empire will be short of a lot of debt and humiliations, and in a superb position to fight back any Japanese attempts, if they dare at all.
Most important is however, that the OTL economical and military vacuum which was created in WWII in the areas of the old European colonial empires will not be present. Not that troubles are absent, but where OTL post-war left no choice for the old colonies/Dominions etc. but to seek US protection and co-operation, they will now need a special occasion/reason to seek away from what they know and recently have experienced do its job.
Canada will anyway need to balance herself finely between USA and the Empire, but as long as the Empire and USA hasn’t any serious quarrels with each other I don’t see why Canada should leave a/the Commonwealth. She of course would be reluctant to military obligations anywhere near bringing her on collision course with USA or economical co-operation limiting her interaction with USA.
India will still have her Ghandi, Nehru etc., but again, if there still is a vital Empire present, Indian economical activity will be with the Empire, business as usual, and India will rather need assurance of this being combined with greater political liberation and recognition, than total separation. I hesitate to say symbolic political changes, as extending basic human right to the Indians is way beyond symbols, but I don’t see why this couldn’t co-exist with the political, economical and military interests of a Commonwealth/Empire.
In the long run this would have tremendous importance for global economy and politics. Instead of OECD countries facing each other and in all practical terms excluding the third world the pre-arranged circles of various interactions will now include both first and third world countries, and the level of investments from first to third world probably will be must higher than in OTL post WWII (with due respect to Nial Fergusson’s work).
In OTL USA went deeper into the interwar depression than Europe, and in this ATL won’t have WWII and the vacuum filling in of the post war period to boost economy. New Deal etc. might still be initiated, but only was the spark plug, WWII and USA’s superpower role was the fuel and engine in USA post war total dominance. USA will still be huge, and probably the biggest single economy, but probably confined to the American continents and (some parts of the) the pacific region. First of all China, but here Japan will the main rival, and the Empire(s) might easily find themselves a good place on a fence watching Japan and USA fighting over the Chinese ruin. The general image might easily be that of happy times for those to be so happy to be part of a Commonwealth to advance within, and misery for those outside.
Regards
Steffen Redbeard