If it is Stillwell, note that several sources misleadingly give the company date as “before 1840”. I don’t know why, but they are all probably feeding from the same incomplete information source.
Edward Stillwell began business around 1825, but “& Son” wasn’t added to the company name until about 1852 as “Edward Stillwell & Son” or “Stillwell & Son”. By 1881 they had directory listings at 25 & 26 Barbican, London EC; 6 Little Britain, London EC; & 29 Savile Row, Regent Street, London W trading as:
“Gold & silver lacemen & embroiderers, army & navy outfitters, cork helmet manufacturers & sword cutlers, Manchester & woollen warehousemen, & every description of Masonic clothing, jewels, furniture & fittings, tinsel, lace & trimmings” and boasted that they had a “prize medal 1862 for good execution”.
They ceased trading around 1957. That particular button backmark show by Matt above is from a pattern 1901-1921 Royal Naval Reserve uniform button.