Yes BSA Slopers (up to 1930 at least) used a pillar mounted seat like this one. Terry claimed to have the patent for the spring saddle, which appeared in the early 1920s (around 1923?). From there it quickly took over from the pan saddle which had been around since about 1913. If the Terry patent was any good, your seat would either be built by Terry, or built by someone else under license from Terry. I think many manufacturers - large and small - would have used a post-mounted Terry from the mid-1920s. By the early thirties the bottoms of the main coil springs were typically bolted to the frame.
Leon