Not purpose built, as they were all modified 'in-theatre' by the SAS to suit what they needed to do, as did the LRDG, and later, some of the Divisional Recce units, notably the 1st Airborne Recce at Arnhem.
SAS/LRDG in North Africa made use of a lot of captured Germanand Italian
kit/weapons if it suited their purpose, but then again so did other units. Scrounging kit of anyone that had something you wanted, was a prime skill of most WW2 soldiers, as the logistics of supply of kit to the front line was anything but good (unless you were US forces).
e.g.
Most kit used by the WW2 SAS as said, was as issued to the Commando's (they were formed first) and later the Airborne troops, including the FS fighting knife, silenced STEN and other toys.