This picture was made available by Ian Frost.
Case: No case, mounted on substantial baseboard.
Movement: The wheel is powered from a master clock and impulsed every 30 seconds (some are pulsed once a minute)
Size: Very approximately 2ft square.
This wheel is very similar, and of a similar age, to the Gents programme wheel also pictured on this website.
A very knowledgable friend has informed me that this is a "Synchronome" Program Wheel, badged for Magneta.