It looks to be an early BSA M20, 1937 or 1938 pattern which differed quite considerably from the later standardised War Department model.
The "C" number that you're quoting is a bit puzling as the pictures I have seem to suggest a change to six digit numbers by 1936. Could there be an extra cipher ? I can't bring any detail up from the IWM on line image. Do you have a better copy ?
Rich
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