There is certainly lots of potential for a Canadian unit to be issued British BD during the winter months in Italy. For the summer months, British or Indian manufacture KD was issued. British manufacture 1937 Pattern Web would also be appropriate with either early manufacture British MK II or Canadian Mk II helmets. Depending on the unit and the situation, the barest of insignia to the full allotment could be worn.
The key would be to make sure that everyone is dressed to a similar standard that that it is known that the reason British manufacture uniforms are being worn was that the clothing was provided from Mediterrainean theatre stores.