The gun has the general appearance of one made in Birmingham by The Midland Gun Company who turned out thousands of guns for the trade. It was made and proofed for 12 bore black powder cartridges and would almost certainly have been made for 2 1/2" length cases. the 14 designation indicated the bore diameter at 9 inches from the breech face was 14 bore when proofed; I have seen 12 bores marked as tight as 15. It could possibly have been lengthened but some live pigeon trap guns were made with 2 3/4" chambers and although this does not have th appearance of a trap gun it may have been made with the longer chambers for some reason. At that time the chamber length was not indicated on the proof marks as such but Midland Gun often marked it themselves on the forend loop on the barrels. The letter 'R' on the barrels may have been a barrel bores mark and that of the Rees brothers who were working for Midland Gun at around the time your gun was proofed.
I have nothing on Stanford & Laxton and suspect that it was one of many rertail outlets that had guns made in the trade and named for them. This was very common practice in the U.K. and does cause a few research headaches. I did research one recently with a name I could not trace and eventually got it down to a Victorian botanical expedition outfitters in London. Lagopus.....
