Yes, that is the Whitworth system. Still in use. Anybody own a British motorcycle?
If they do, they know that those wrench sizes changed around the middle of the last century.
Whitworth and American (SAE) wrenches, although marked with the same bolt size, would have different size openings. I have both in my collections, and you can easily see the difference. Although Whitworth wrenches are marked with the bolt size, that is where the similarity ends. I have both types of wrench. American industry used an (old designation "USS" or "SAE") ASME UNC bolt. British bolt head sizes are different.
A UNC 3/8" nut is 9/16"across the flats. Whitworth bolts measure ~23/32" across, ~5/32" bigger. Well at least in that time frame. The Whitworth standard changed in 1951. Then a 3/8" bolt would have a 29/32" head.
It kind of helps explain some of those weird **/32" socket sizes, eh?
The United States did not adopt Whitworth as a standard, ever. I would argue that the Whitworth Wikipedia article is misleading. The Wikipedia "Screw Thread" wiki is more accurate in the discussion of Whitworth thread use in the US : "During the 1840s through 1860s, this standard was often used in the United States and Canada as well, in addition to myriad intra- and inter-company standards."
From the ASME website, about the USS/SAE/UNC fasteners.:
"But by the 1880s, the system had triumphed, as machines with interchangeable parts — from typewriters to locomotives — flooded the national economy. Known originally as the Sellers or Franklin Institute threads, they became the United States Standard threads. Other systems of screw threads have since come into widespread use. But down to the present day, William Sellers' innovation remains a ubiquitous standard. Take a quarter-inch nut from a Portland, Maine, hardware store and it will reliably fit a quarter-inch bolt in Portland, Oregon. The economy and simplicity of this elegantly rational system represents William Sellers' legacy and the enduring quality of fine mechanical engineering."
Unlike other American innovations like fast food restaurants, I don't think the "triumph" lasted that well. Metric standard seems to be the winner.
Chilly