Hi Marie,
James Hardy & Co were an old established business that started in Aberdeen and expanded to Edinburgh and London.

James Hardy & Co. - Aberdeen - 1894
The London branch was sold off in 1897 to William Duncan Cooper who continued to trade there under the James Hardy & Co. name.
James Hardy entered marks at the London, Edinburgh, and Glasgow assay offices. They were still in business in the 1980's.

The 7385 number on your cruet set would probably relate to the pattern.
If you can capture a good image of the marks we would appreciate them for the Encyclopedia.
Trev.