If those are 8 bore shells, that isn't an 8 bore gun. They're bigger than the OD of the breech.
I can tell you this about the company. It was founded in 1833 by William Moore. In 1844 William Grey joined the company and it was known as Wm. Moore & Grey. In 1908 it was bought by Cogswell & Harrison. Both Moore and Grey had previously worked for Joseph Manton....along with about 1/4 of the renowned makers in England. They were located at several addresses over their life.
There was also at least one other maker using that name and, possibly 2. As in Germany, at that time, gun making was often a family affair, to include intermarriages between the families.
At that time a lot of "London" guns were made in Birmingham. Many were also sent to London for proof so it would bear London proof marks rather than Birmingham. London made guns were supposed to be better...even if made in Birmingham.