I have search the Blue Book, Standard Catalog of Firearms, Gun Digest Book of Guns and Prices and all of the online auction sites and there is one listing for A. Allan. on guns America. The sale price is $1000 and this gun needs some minor work. http://www.gunsamerica.com/995420860/Guns/Shotguns/Double-Shotguns/English/Arthur_Allan_Glasgow_Boxlock_Fowler.htm
Most Damascus barreled guns were made in the 1880's and 90's and very early 1900's. The patterns in the steel can be beautiful. They should be shot using black powder loads only. There should be a crown with letters under it stamped somewhere on the barrels for the black powder proof.
Comparing prices on other English made shotguns, a double in very good condition with some engraving should sell for around $1500.
I hope this helps you,