Just lost a post I was typing at for over two hours.
It included reference to that link, which is one of several resources out there that can give a nice picture of the RAF around the time of the Battle of Britain. If you want to work back to May/June, then the production figures are available.
For the RAAF, I had a comprehensive run down. I won't tempt fate by repeating it all here. The squadrons in service were 1, 2, 3, 4, 5(rebadged as 9) 6, 7, 10, 11, 12, 13, 14, 21, 22, 23, 24 and 25. They were a mixture of some fighter squadrons, a majority of bomber squadrons and 3 seaplane squadrons.
3, 4, 21, 24 and 25 were the fighters with Gladiators in North Africa; Wirraways in Canberra; Wirraways in Melbourne; Wirraways in Townsville; and Wirraways in Perth respectively.
1, 2, 6, 7, 12, 13, 14, 22, and 23 were the bombers, equipped in the main with Avro Ansons.
9, 10 and 11 were the seaplanes, equipped with Seagulls, Empires and Sunderlands. 10 Sqn, with Sunderlands, was based in Britain.
Italian Infantry: I think it is justified in terms of performance and various intangible factors that cannot be properly included in the game. There were always exceptions in the case of individual units.
RM:
"At June, 10th, 1940 (at the very beginning of the war) the Regia Marina was composed by
◊ 6 battleships, two of them of modern 35,000 ton. type
◊ 7 cruisers of 10,000 ton.
◊ 14 light cruisers between 5.000 and 8.000 ton.
◊ 12 flotilla leader destroyers
◊ 28 modern destroyers
◊ 19 old model destroyers
◊ 69 torpedo boats
◊ 117 submarines of varied type and tonnage"
http://www.regiamarina.it/eng_index.htm
The orbat in the game at the moment lacks the two Littorios, leaving
4 battleships (two less than @)
7 heavy cruisers (correct)
12 light cruisers (2 less; additionally Capitani Romani CL/DLs effectively can fit in this category, or more properly as warbuilt cruisers. The missing units are the old Taranto and Bari.)
12 destroyer leaders (these ships, the 12 Navigatori class, could be simulated in the short terms with veteran 1939 destroyers, appropriately badged)
60 1939 Destroyers (32 more than @; however, refer to the above DL caveat)
28 WW1 Destroyers (9 more than @)
92 Submarines (25 less than @)
I do not think that torpedo boats should make it, even under the guise of WW1 destroyers. There is enough of an equalizer in the submarine arm. If they have to make it in, then sloops, frigates, TBs can all be incorporated under the sub chaser unit, re-named Destroyer Escorts, and made available from the start. That way, it won't muddle the numbers, as could happen with the RM or KM.
The RM is a strong force as long as it doesn't fritter away its power against the MN Med Fleet before France is overrun. If it does this, then the RN can easily pick off the remnants, and there goes Italy's war.
Light Cruiser names:
http://www.regiamarina.net/arsenals/ships_it/cruisers_light/crui_light_us.htm
Destroyer names:
http://www.regiamarina.it/ordbatteng.htm
In fact, that will give you a perfect orbat for the whole kit and kaboodle at 10 June. It has fleets, bases and even divisions of area:
http://www.regiamarina.it/organization.htm
There is a question of Richelieu and Jean Bart. The first should definitely make it; the second was not complete when she sailed.
Including the other two as a production option, and even the Alsace class is an idea, given the presence of the H-class and its ilk.