Help with ID and Accessories

[Plymouthbel]

Hi Guys,
I am trying to identify what I have been told is a Birmingham Shotgun.
There are a lot that look close to this one but nothing exactly the same that I can find on the web so here I am.
Long story short, is has been in the family for many years and is treasured by my father. He has been given a short time to live so I want to fix it up for him so the starting point is finding out what it is then I will be looking for the parts to fix it up. I am not planning on getting it working just back to complete.
Wilson on the lock is my surname, we dont believe that its the company that made it.
Also I have the original box that I am trying to repair after it has been sitting under houses for over 100 years. I want to find out what it would have looked like and what it would have included. I have the cleaning rod and the oil can but thats it and the box isnt lined.

Here is a few pics and thankyou in advance as any hints will be greatly appreciated.