Judging by a google search, "Ensign" seems to have been more common as a model name than a brand name. It looks like a 1960s Swiss made automatic watch with a tarnished gold-plated case, mold on the dial and the luminous paint missing from the hands. No particular connection with the British Army so far as I can see. Do you have a photo of the back?
As the word automatic is written in French, the watch is most likely from the French part of Switzerland and the only company which had been registered in the French speaking region there, using the 'Ensign' brand name, is Record Dreadnought Watch Co. SA, Tramelan-Dessus and La Chaux-de-Fonds, Switzerland.
Otherwise, this image shows not much, I wonder if there is a 'made in...' below the 6. Pictures of the back and possible the movement would tell more. So far I am only certain it is a wrist watch.
Dreadnough became Record Dreadnought Watch Co., after the merger with offices in London. Record made official watches for the German and British army, which would be a lead if the watch had been owned by a member of the British Army.
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