I looked in the newspaper archive for firms advertising jobs for satin liners in the 1930’s in Sheffield. Several were for the cabinet case trade, one was for the cutlery case trade, and one was for a cap maker.
Ancestry has transcribed the occupations in the 1939 register and you can therefore search in keyword.
There are 8 hits for satin liner, all Sheffield.
Satin liner cutler 1
Cutlery case satin liner 1
Satin liner 2 (includes Rose Holmes)
Satin liner cutlery cases 1
Cabinet case satin liner 2
Satin liner cabinet cases 1