Keith,  According to Jean-Claude Piguet in his book, "The Music Box
Makers", Barnett H. Abrahams, who had a sales network in London, went
to Switzerland and opened a company to manufacture disc musical boxes.
He was in business at No. 3 Rue des Artes in Ste Croix, Switzerland,
from August, 1895, until 1904, and then his sons, under a new company,
Britannia, S.A., for less than one more year, ending January 18, 1905.
So your music box would have been made sometime during that ten year
period.

Their products were first sold through his London network, "Star Silver
Depot", under the name Imperial and then under the name Britannia.
Britannia and Imperial use the same diameter discs interchangeably.
I don't know of any surviving records showing serial numbers of
machines and when they were made.

Here's a thought.  If you knew what the largest serial number of this
size was and assuming that production of this size musical box was
steady over the ten years (although that may not be realistic), then
you might be able to make an educated guess as to the actual date of
manufacture.  Perhaps readers could weigh in with serial numbers of
their 9" Britannia and Imperial musical boxes.  With enough serial
numbers in such an informal census it might be possible to narrow the
date down.  Whether accurate or not, it would be interesting in any
case.

Bill Wineburgh
http://antiquemusicbox.us/