Non-US involvement in Downfall and related operations would have been very extensive, more than a million men in total. I've picked out three "big ones" down below, but if I've missed anything else I invite others to correct me:
1.) A huge Royal Navy fleet. Plans dating from Spring 1944 envisioned 5 fleet carriers, 5 light carriers, 6 battleships, and 25 cruisers for the Pacific Fleet alone, not counting the smaller East Indies Fleet. Another estimate mentions up to 12 British carriers in total (the Japanese expected the RN would bring 13 carriers, 4 battleships, 8 cruisers, and 40 destroyers). Overall close to 90% of the Royal Navy's 866,000 officers and men, along with virtually the entirety of the Commonwealth navies, would be committed either to direct operations against Japan (which also probably included the planned landings in Malaya) or to securing lines of communication in the Pacific and Indian oceans. At this time the French presence in the Pacific ocean was also starting to become substantial, though I can't recall anything dealing with their actual involvement against the Japanese mainland.
2.)
Tiger Force, an Anglo-Canadian bomber force based on Okinawa. By 15 August 1945 it was assigned 22 bomber squadrons along with miscellaneous support (communications, air-sea rescue, and so on). Additionally about 15 squadrons' worth of tactical aviation were also on the table.
According to the source, the TO&E breakdown of aircraft to be committed by country for the strategic bomber force (not including the tactical aviation) would be as follows:
- RAF: 130 Lancasters, 20 Lincolns, 40 reserve bombers (either Lancasters or Lincolns), 50 Mosquitoes, 10 Catalinas, 9 Austers, 3 Expediters
- RCAF: 40 Lancasters, 120 Lincolns, 3 Austers
- RAAF: 20 Lancasters, 20 Lincolns
- RNZAF: 20 Lancasters
Total: 210 Lancasters, 160 Lincolns, 40 reserves (either Lancaster or Lincoln), 50 Mosquitoes, 10 Catalinas, 12 Austers, 3 Expediters
According to D.M. Giangreco, 34,890 RAF personnel were to be transferred to Okinawa along with an initial contingent of 10 squadrons, down from the 96,000 men envisioned for the original plan where the force was to be based out of Cagayan Valley in the Philippines. According to this idea the US Eighth Air Force, also to be based in the Ryukyus, would be able to relieve some of the logistical burden, especially in engineering, which would allow for a smaller manpower commitment.
3.) The Commonwealth Corps:
This is a bit convoluted so bear with me:
The "Commonwealth Corps" started as a proposal from the British Chiefs of Staff in July 1945 for a 3-5 division contingent for the invasion of Honshu, Operation Coronet. Before this, the US already accepted the participation of a Canadian division (the 6th Infantry) and was separately considering the offer of an Australian Division [
JCS 1388/4, 11 July 1945]. The "surprise" offer of the Commonwealth Corps caused a disturbance in the original plan for the 6th Division, which was for the unit to be directly integrated into an American corps for the purpose of forging closer ties between the two countries. The UK's proposal meant this idea would be scrapped in favor of putting the 6th Division under a more "British" command structure.
Likewise, existing plans for Australia's involvement probably would have been integrated into the Corps. In his book, D.M. Giangreco mentions that General MacArthur wanted the powerful Australian I Corps (6th, 7th, and 9th Divisions) for Honshu, which at the the time was engaged in the reduction of Japanese resistance in Borneo and Melanesia. However, Australia's partial demobilization after the defeat of Germany temporarily reduced their commitment to only one reinforced division (the 10th, which would have been amalgamated from existing forces), and Giangreco speculates that ultimately no more than 1-2 Australian divisions would have been involved. Besides this, New Zealand was also determined to include their 2nd Division and was pushing hard for this when the war ended. As mentioned above, the original proposal also included an Indian division from SEAC, but MacArthur vetoed it on linguistic grounds.
From all of this, we can form a fairly good estimate of the force's composition, at least at the divisional level:
- HQ: Lt. Gen. Sir Leslie Morshead
-- UK 3rd Infantry Division
-- 6th Canadian Infantry Division
-- 2nd New Zealand Division
-- Australian 10th Division
-- possibly one other Australian division
Using Army Service Forces' rule of thumb, during the assault phase each division would have a "slice" of 25,000 men and 4,000 vehicles, to be reinforced to 40,000 men and 7,500 vehicles after build-up. This corresponds to a total of 100,000 to 125,000 men and 16,000 to 20,000 vehicles during the assault phase and 160,000 to 200,000 men and 30,000 to 37,500 vehicles after build-up; a considerable force by any measure.
It's also worth pointing out that by July 1945 France also offered a corps of two colonial divisions for operations in the Pacific. JCS 1388/4 indicates that at that time considerations were underway as to where and when these forces could best be put to use, though again Giangreco and others make no mention of French troops being involved in the invasion of Japan proper.