I think it unlikely that these bolts were " made in the machine shops of BSA itself".
I lived and worked in the Midlands for a few years shortly after the demise of BSA and even then I was surprised and a little charmed by the existence of the traditional industries seemingly unique to each village. Wednesbury for locks, Dudley for chains, Bloxwich for metal stampings, engine blocks were cast in Wolverhampton, and nuts and bolts were made in Darleston. Each small industry provided the pieces for the large manufacturers. I worked in several, even the upholstery for Leyland Cars was made in small factories.

The demise of the large auto producers, both car and motor cycles, was devastating to not just the actual communities around the assembly plants.

I think it much more likely that the domed bolts, in all their array of threads, were bought in. In the glory days of the '60s, with little competition, the extra cost was nor particularly relevant. They were abandoned about the same time that using the "right" thread, was changed to using the "cheapest" thread.