Hi,
Not all BSAs had a serial number as BSA supplied blank trigger blocks with aperture sights as replacements upon request. For instance, I know of a .25 Improved Model D with no serial number but in every other respect, the rifle is correct. Does yours have an aperture sight or space for one in the trigger block?
I suspect the first two characters on the sight are RD. With the stock length, I suspect you have a Light Pattern from around 1910-1914. Sorry, can't access your pics.
Kind regards,
John