Once well-known in the United States for their range of small, plain milling machines, The Burke Machinery Co was incorporated on December the 3rd. 1903 becoming The Burke Machine Tool Co. on October 24th in 1911.
Although advertised under a number of "assumed" names by various British machine-tool agencies during the 1920s and 1930s, it was not until WW2 that any great numbers of these unadorned, simply-finished millers entered the United Kingdom. Although a  range of sizes was offered, the No. 0 shown here was the baby of the range and is now probably the hardest to find.
Of the "stub-milling" type with no overarm to support a long cutter-holding arbor, the body and head were cast as one rigid structure like the similar machines from, for example, Stark,  Pratt & Whitney (with their Size 00), Van Norman,  Benson, Carter & Hakes,  Schaublin, Leinen,  Sloan & Chace, American Watch Tool Co.,  Waltham and Barker. However, all these differed from competing machines from manufacturers of precision bench lathes, including Cataract, Ames, Lorch and Mikron, who employed a rather expensively constructed lathe headstock fitted to a suitable base and table assembly.
Equipped with all-lever feeds to the tiny longitudinal and vertical movements (4 inches and 3.25 inches respectively) and just 1.5 inches in traverse by a screw, this was a milling machine intended for the production of small components - probably incorporating the use of simple jigs and a long-suffering woman operator. 
Photographed in its restored state with a V-pulley on the plain-bearing spindle, the miller would originally have been driven by a 3-step flat-belt cone pulley, almost certainly from a factory's overhead line shafting..