Just found a bit about the place.
The Hungry Man was on the corner of King Alfred Place, in front of the new Bham Rep Theatre, and it was a beerhouse for many years in the 19th century - No 24 Broad Street after the mid 1970s, No 20 before. In the 1930s it became a licensed restaurant, which it called itself until it closed in the 1960s.
Here are extracts from some Kelly's Directories:
1873 - 20 Broad St: Edward Roberts, dining rooms
1879 - [Beer retailer] Mrs Emily Richards - [Post Office]
1895 - [Beer retailer] Mrs Agnes Eaton
1921 - [Beer retailer] Herbert Sprawson
1933 - [Beer retailer] Isaac Roberts
1937-1963 - [Licensed restaurant]
1969 - not mentioned (site of new Rep) Theatre
Hope that is of interest.
Peter