Vox black plastic control knob, part number 09-703-0, used for volume and tone controls on JMI-made Vox guitars from 1962 until at least 1965 - typically on three-pickup guitars such as the Dominator, later versions of the Shadow, the Super Ace and Apache. These are all guitars made in the United Kingdom; Italian Vox guitars didn't use them. Later examples of these guitars were generally fitted with the metal control knobs.
The images below show an unmounted knob, with grub screw. Diameter (at base) 19.2mm, height 13.7mm. Grub screw, slotted head, 3.5mm x 6.5mm.
From the underside, it can be seen that this part is identical to the far more widely used white version.
The controls of the 1964 Vox Shadow, below are a little atypical. The controls actual function are not straight forward for this guitar: basically a master volume, and separate tone controls for the middle and neck pickups. Read more, and listen to soundclips of the different pickups here.
List of Vox control knobs