Woodward is one of the most expensive, finest made shotguns in the world. In fact, in the "old money" uber shotgun world, the true collectors and aficionados prefer Woodwards, MacNaughtons, and Dicksons to the "big 4" of Boss, Purdey, Holland, and Westley.
I don't recall seeing any Woodward double rifles over the years so if they did make some, they surely made very few. Woodward was most famous for a lightweight over/under game gun when SxS was a hundred fold more popular.
To the other points in the thread, everyone is wisely pointing out that there were a lot more retailers than actual makers with a gun works. Holland didn't even have a gun factory until 1898 yet people pay ridiculous money for Scott Dominions and Climaxes that say "H&H" on the rib. Manton was dead and buried by around 1850 and the name was used on working quality guns for sale in India in the 20th century. Almost every maker has a similar story pointing to them being merely a retailer (or stocker/finisher).