don't know if this one was followed through, but haven't seen any further information or images posted so perhaps not.
The following comes from The National Archives book of Designs ref. BT 45/26/5194 - which as indicated by Anne, is not one of the usual Board of Trade Registrations.
Typically, British Board of Trade Rd. Nos. are represented by an image in one book, with details of the Registrant in another, and generally these are non-functional items that are decorative and lack complexity, or have very simplistic and very obvious function.
Items such as this Blumberg Night Light require some explanation due to their intended mechanical function, so seem to end up in a separate book which I think was categorized as useful designs.
The text is a beautiful copper plate hand, but probably illegible on the screen, so have transcribed as below:
""The purpose of utility to which the shape or configuration of this design has reference, is that a night light may be placed with facility upon any description of candlestick, and that if desired it may be protected by a glass and be carried about without any inconvenience.
Description.
The drawing exhibits five views of the design drawn full size - Figure 1 being an elevation - Figure 2 a section through a line CD - Figure 3 a plan.
Figure IV an inverted plan, and Figure V the design fitted with a glass globe.
A indicates a cup formed by the rim a and plate C to receive the night light, whether a child's night light floating in water or simply oil and a wick - B tube fitting into a candlestick of any description- the socket of which exceeds in diameter that of the tube B and does not that of the plate C.
D flange to support a globe or glass of any shape.
The design may be made of metal, porcelain, glass or any suitable material . If of metal, the inside of the cup A may be coated with porcelain or glass or be fitted with a cup of analogous material. The part B may be a hollow cylinder or a solid item. The whole of the design is new and original as regards the shape and configuration thereof.""
Obviously not the sort of decorative collectible night light that we're accustomed to seeing - possibly, even, not collectible in any sense, but hopefully will take the worry out of the collectors nightmares, who might be thinking they're missing something very desirable
As always some loss of clarity due to the watermarking.