The first Dandys left the factory in October 1956, although the plan was for an earlier launch.
Yours is an early one, with Wipac electrics.
There were a lot of problems with the Dandy. Around 1000 of the first made were recalled to supplying dealers, and those which made it back to the dealer had their frames changed. I dont know what the problem was, but there is a book in the factory despatch records which lists those which were changed. It is a possibility that your Dandy had the frame changed and that the dealer failed to stamp it, or it could be just covered with paint.
There were around 14 factory to dealer service sheets issued over the next 3 or 4 years detailing changes and modifications to the machine.
I have attached one such service sheet to give you the flavour, also attached is the front page of the Dandy brochure issued around the time yours was sold, and a page from 1956 owners manual.
The BSAOC magazine, The Star, June and July 2016, has interesting Dandy articles written by Dr Arthur Dawkins. They are well worth reading.
Also see Dandy post earlier this year.