I do believe the bulk of the Australian Allied support was based in North Africa, with some in Greece or Crete. Google 'Rats of Tobruk' for a quick example
en.wikipedia.org/wiki/Eighth_Army_(United_Kingdom)
The 8th Army was a 'British Army' consisting of many units from a range of Allied countries.
All ultimately under the command of Montgomery.
The Eighth Army was formed from the Western Desert Force in September 1941 and put under the command of Lieutenant-General Alan Cunningham. At its creation, the Eighth Army comprised 7th British Armoured Division and 4th Indian Infantry Division.[12]
By November 1941 it had expanded to two Corps: XIII Corps under Lieutenant-General Reade Godwin-Austen[13] and XXX Corps under Lieutenant-General Willoughby Norrie:[14]
XIII Corps composed of the 2nd New Zealand Division (commanded by Major-General Bernard Freyberg),[15] the 4th Indian Infantry Division (commanded by Major-General Frank Messervy),[16] and the 1st Army Tank Brigade (commanded by Brigadier Watkins).[17]
XXX Corps was made up of 7th British Armoured Division (commanded by Major-General William Gott),[18] the South African 1st Infantry Division (commanded by Major-General George Brink),[19] the 4th Armoured Brigade (commanded by Brigadier Gatehouse) and the 22nd Guards Brigade (commanded by Brigadier Erskine).[17]
The Eighth Army also included the Tobruk garrison which was supported by the 70th British Infantry Division (commanded by Major-General Ronald Scobie) which included the Polish Carpathian Brigade.[17]
By the time the army was fighting the Second Battle of El Alamein, it had reached a size of over 220,000 men in 10 divisions and several independent brigades.[20]