Indeed, but based on the letter which suggests his family were engaged in the horse trade, or similar, you would expect them, a family by the name of Mills, to appear on the 1939 Register with a connection to horses etc.
Also, the Cambridge Archives have searched the 1938 - 40 Spalding’s Directory and Kelly’s Directory of 1948 for horse slaughterers, dealers etc by the name of ‘Mills’, their efforts have produced a nil return. There do not appear to be any families by the name of ‘Mills’ engaged in the equine industry in Cambridge during the period 1938 - 48, according to the efforts of the Archives.