Hal's pictures show a mid-level quality 10 bore, proofed in Birmingham, with the name on the side plates appearing to be indeed D e w s o n. The barrel maker was "TB." So since no-one can identify a gunmaker named "Dewson," one guesses for now the story stops here. Interesting search and this type of thing is always fun. Perhaps a look at the UK newspaper database and a search for "Dawson" might turn something up.
[Linked Image from i.imgur.com]
[Linked Image from i.imgur.com]

Baluch are not Brahui, Brahui are Baluch