you'll find the history of this bike tied with the history of BSA, acquired by BSA in 1943, and separated from the motorcycle business in 1953
they were acquired by Raleigh in 1957 - may have been made in to the early 60s, but no specific information.
I would be trying to date this bike to between 1953-57, before Raleigh bought BSA/Sunbeam bicycles.
Though the Made in England script sure matches Raleigh script.
Must be one of the rarest headbadges out there.
Right - it's a Raleigh-made 3-speed light roadster with the Sunbeam badge. The four bands usually mean an AMF bike sent to the US. The bikes have the Sunbeam badge but are unrelated to the original, pre-Raleigh merger Sunbeam.