Looks very much like Jobling's 2497 'Cigarette Box and Ash Tray Combined', though the one shown in the 1937 catalogue is plain with no writing.
I have previously seen an example with a different logo on, presumably made as a special commission. Jobling also list a 2555 'Decorated Ash Tray and Cigarette Box' which is the same shape and size but with an geometric/ art deco design on the sides.
Anyway, Jobling would be my suggestion, as the shape is so distinctive. However, it's possible these boxes were also made by other firms: Jobling don't appear to have registered the design.
Steven