There were literally hundreds if not thousands of gunmakers in the birmingham gun quarter over the years, many would have been very small concerns, maybe a couple of gunsmiths working together in a workshop rented from birmingham council or a larger gunmaker. I was looking for information on a reasonably large gunmaker called s.wright in birmingham , they were contractors for a lot of other well known makers, information was virtually non-existant.
There is or was a london maker called james roberts. Have you tried the birmingham history forum ? They are very helpful and someone might know.
another possibility is that the gun was made by the trade and retailed by someone called james-roberts , this happened a lot , army and navy csl being a good example , the guns were marked with their name but were usually made by westley richards , bsa or webley etc.
http://www.jroberts-gunmakers.co.uk/