Not a W.J.Jeffery (William Jackman Jeffery) as he was always listed at London addresses. He never made guns but always sourced them from the trade.
What you have is a W. Jeffery. Now comes the puzzle as I can find a Jeffery at Plymouth but not at that address and listed as A.R & H.V Jeffery. They were in business only for a short while between 1966 and 1976. I suspect your man was a relative or had some connection. A good picture of the barrel proof marks may shed a little more light. It certainly looks as if it started life with Webley & Scott. Is it an ejector or non-ejector? Lagopus.....
