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I found a zither banjo in an antique store in of all places, Marion Illinois.
How common are Barnes And Mullins No 2 Perfect zither banjos? how much are they worth? Do they have serial numbers? I know that they were made in England. I think that they were made between 1900 and 1910. It it in wonderful condition.
The real expert on here is David Wade, so maybe he can comment.
His website gives details on Zither banjos http://www.zither-banjo.org.uk/
As far as I am aware Barnes and Mullins zithers were generally of a lower grade (with some exceptions) and not of great value. From the photos and the condition, your instrument "looks" to me that it may be worth in the region £100 or maybe even much less... but as I said, Dave will give a better idea of value.