The 'direction arrow' on the blackout mask is the Board of Ordnance/War Dept/MoD
'Broad Arrow' mark, which would imply it was produced for a military contract. There are a number of identical lamps (all missing the blackout mask, which makes yours quite rare, I expect) currently listed on ebay and various
militaria/antique sites as WW2 British Army/military railway signal oil lamps, though they carried on being made for the military post-war (there is one listed on ebay dated 1954). They have a tube attached to the upper 'pie crust' chimney section that fits over the burner which carries the filters for the 3 signal aspect colours.
It appears that contracts were let to a number of manufacturers, mostly around the metal-bashing area of Birmingham such as Wakefields, Chapman Bros., Harry J. Pratt & Co and C. Eastgate & Son. There should be an oval stamped manufacturer's plate with the broad arrow mark and the year of manufacture tack welded or soldered on the side.
The other pair of lamps are
WW2 military 1941 pattern candle lamps made by T.E, Bladon & Sons of Birmingham, though I think the basic design sans the blackout shade dates to before the war (they are sometimes listed as WW1 trench lamps).