The flying column, Kingcol

Brigadier Kingstone, commander of the 4th Cavalry Brigade led Kingcol, the "flying column" that that move the 500 miles across the desert. Kingcol had about 2,000 men and 500 vehicles, and was a combined-arms force, according to the current parlance. The units that comprised Kingcol were:

HQ and Signals, 4th Cavalry Brigade
the Household Cavalry Regiment
237th Battery, Royal Artillery
one anti-tank gun troop, Royal Artillery
one troop, 2nd Field Squadron, Royal Engineers
one detachment from Boring Section, Royal Engineers
two companies, 1st Essex Regiment
a detachment of the 166th Light Field Ambulance
3rd Reserve Motor Transport Company, RASC
552nd Motor Transport Company, RASC
8 armoured cars from  No.2 Armoured Car Company, RAF

This is based on the account and information in Vol.II of the Official History of the War in the Mediterranean and Middle East.