I think that if, as you describe, the family were still in the printing business in Birmingham to the 1940s, then the firm must have changed their name or have been taken over before the first war. Examination of the directories shows no entry in the 1862 edition in Bromsgrove street , or elsewhere, for a printer named Stevens, but, as the entries usually refer to the year before then he could have started there in late 1861. In the 1868 directory George Stevens, letterpress printer is at 10½ Bromsgrove St, but by 1872 he has moved a few doors down to no 19. He remains there till sometime between 1884 and 1888, when the business is listed as belonging to Mrs Ann Stevens, presumably his wife. It remains in the directories under her name till the 1904 edition, but has gone by 1912. There seems to be no listing for a Stevens printer in that year or in 1921 or 1933, which is why I believe the firm probably changed its name or merged, presumably when Ann died.
Mike