Well, the Lend-Lease Savage made No. 4 rifles were certainly used. They were of Britishpattern, though.
In general terms, the Lend-Lease arms were reserved for secondary use, freeing up the standard British types for front line service.
The 300,000 Thompsons ordered in 1940 were paid for using gold reserves, at 45-50 Pounds Sterling each. Only 100,000 reached Britain, the balance being lost in transit. The Thompsons were extensively used by all Commonwealth forces. Britain was broke, and the importance of Lend-Lease cannot be underestimated.