While I have my "Lightweight Cycle Catalogues Volume I" out, yesterday Kelvin Pawsey asked about CB serial number "646 23 DC". The book does not show anything quite like that format. The closest I see is "569 3959", which means September 1956, frame #3959 produced that year. It looks like 6-digit numbers were used before 1951 and from 1958 on.
The "real" Claud Butlers ended in 1957 and were acquired by Holdsworth in 1958 and then by Falcon Cycles in 1987. That's all I know and I don't claim to be an expert other than I had one in 1953 and am restoring a 1951 model right now. Hilary Stone would be as knowledgable as anybody on this list.