This trooper is about to depart Kufra and therefore is clean shaven. His hat is the field service cap* for a Battle Dress (BD) uniform. This cap was common among most units in the British Army.
The troopers basic uniform is the Khaki Drill (KD) shirt and shorts. He also wears the the popular service pullover over the KD shirt. The pullover had a "Vee" neck and epaulettes so that badges of rank could be worn with slip on shoulder boards.
LRDG troops were not always bearded. When they had the chance they would shave. The chance did not come up on patrol too often.
The soldiers wears the 1937 pattern web belt with a compass pouch attached. The Prismatic compass was a valued item and for this reason a lanyard is attached to the compass and it is secured around the troopers neck.
A set of MT goggles is also loosely secured to the web belt.
Chapplies protect the troopers feet. His weapon is the beloved SMLE which is protected against the sand and dust with a snap cover over the bolt and trigger action and sock over the barrel.
* While officially known as the field service cap, it is more commonly known as a "side cap" or "forage cap"