A friend found this among his late father's effects:
At first, he thought it was an old flashlight, but it has a telegraph key at one end. Turns out it is a Morse code signal lamp. Staff at the Military Communications and Electronics Museum in Kingston identified it as a naval unit based on its black colour, and the stand on the bottom for steadying it on a flat surface during use. (The units issued to the army were green, and lacked the stand.) On the battery box it carries the British broad arrow. Other features identify it as World War II vintage (cold war items were made of plastic).
I can find very little information on the manufacturer, Shimwell, Alexander & Co., Ltd., other than that they specialized in military lighting including flashlights, signal lamps and inspection lamps. In the London Gazette of January 1957, they are listed as electrical engineers holding Royal Warrants of Appointment to his Late Majesty King George VI. (Perhaps the King enjoyed signalling his subjects from one of the windows of Buckingham Palace?) The company was still in business in the early 1970's, but seems to have been dissolved not much later than this. Based on Google Maps Streetview, it's location at 13 Bury Street seems to be a residential neighbourhood now.