Hi there. Your mystery badge probably dates pre-world war 2. Prior to 1937 Hornby invited any owner of a Hornby Train Set to become a member. An official application form was filled in and sent to Hornby headquarters at Binns Road, Liverpool together with 6d in stamps in payment for the official badge 'The Hornby Railway Company'. This 'club' was divided into two sections - Senior, for members aged 12 and upwards and Junior for members under 12. A special booklet dealing with model railway working was prepared for each of these sections. Hornby announced that the 'club' was formed for the sole purpose of enabling all Hornby Railway owners to obtain 100% fun from their hobby. When a boy became a member he obtained the great privilege of expert advice entirely free on all the problems that arose in connection with his own railway...
Hope this is of some help to you.