First Canadian Parachute Battalion regularly carried Thompsons.
They were also notoriously known for using captured enemy weapons, to their advantage.
Since 1 CanPara was under British control (i.e. 6th Br Airborne Division), and since AB troops were considered "Bastard Sons",
perhaps many an officious eye was cast aside in view of their battlefield successes.
Yea they might have had some leeway in their choice of personal weapons. Take a look at these:
http://perthregiment.org/rperth6.html



You have a trooper with a SMLE in NWE 1944 and M1 Garands in the hands of several others in Germany 1945. Perhaps the FSSF guys who were folded into 1 Can Para got to keep their M1s...but that really doesn't seem like something the Americans would do