I am far from an expert but I remember Grays of Inverness quite well. In my youth they were one of 3 gunsmiths in Inverness and the only one that had a selection of guns way out of my price range. I would think that anything bearing their name would be Birmingham made but generally of good quality.
They were in business c. 1901 to c.1988.
Their premises is now a bar called Gunsmiths so the memory lives on.