Hi Lugz!
I can help you a bit here, as those King **** wrenches are quite common in the U.K.
Firstly, the wrench shown in your BSA diagram is almost certainly a King ****. The tell tale features are that the slot is on the other side, compared to the Billings, and the adjuster is grooved. From the proportions I’d say it was a 6 inch, but you’d need to print and scale the diagram to be sure!
Also, there’s no way BSA would have provided an imported tool! Nothing to do with patriotism, and everything to do with cost and availabity!
Those King **** adjustables were actually of very good quality. The jaws are much more rigid than the ‘Swedish pattern’ we tend to use now, and they are very usable. I have a couple around, and there’s definitely one in my Dad’s plumbing tools box, that he used to use regularly!
If you want one, I can probably find you one. The post war ones were no different, as far as I have noticed, to the war time ones. May be able to find you a war dated one, but the only way you would know was if it was a government contract tool, and thus marked with a date!
Edit - just noticed page two of this thread, covering a lot of this!
With regard to the original origins of the design, my Grandfather (long departed but the authority on all things tool related) always referred to this pattern as a ‘Billings adjustable’ despite his being made, as far as I’ve found, by King ****.