In April 1939 Page applied for a patent (#529,580) "Improvements in Toy Building Blocks" which was accepted in November 1940. It described hollow square bricks with 4 studs on top. Page offered the cubes for sale from September 1939.
From GAMES & TOYS September 1939
A NEW MATERIAL FOR TOYS, FOR BABIES AND YOUNG CHILDREN By Hilary Page, Managing Director of KIDDICRAFT LTD.
Early in September we shall have another one ready which will be known as Bri-Plax Interlocking Building Cubes (2s. 11d). Building cubes have always been "favourite" toys during the first five years, and Bri-plax building cubes are similar to the ordinary stained and polished or enamelled ones, but by means of a very simple, but very effective device, the cubes will all lock together so that a young child can build them up into quite a high tower without them falling down.
This initial patent was followed by a series of subsequent patents describing 8-stud bricks and baseplates. In 1947 he patented the ‘Self-Locking Building Brick’. Although he successfully protected the design against a UK infringement in 1950, the design was adopted and adapted by Lego to become one of the greatest toys of all time.