The Desert Air Force

The Desert Air Force, at the time of Tobruk's fall, had 22 fighter squadrons, two tactical reconnaissance squadrons, and four light bomber squadrons. The aircraft were a mixture of British made and American made aircraft:

Fighters
11 Hurricane squadrons
6 Kitty Hawk squadrons
1 Spitfire squadron
2 Tomahawk squadrons
2 Beaufighter squadrons

Tactical Reconnaissance
1 Hurricane squadron
1 Tomahawk squadron

Light Bombers
2 Boston squadrons
1 Blenheim squadron
1 Baltimore squadron

The Desert Air Force had 463 aircraft on 22 June 1942, with another 420 distributed across the Middle East. This is based on the account in Vol.III of the Official History.