Electoral Rolls available on this site
Electoral Rolls are useful in locating where a household is living at any point in time. For the period since the date of the latest census available for public viewing (1901) they are probably the most complete list of the population. Over time, the qualification for voting has changed as summarised below.
Date Qualification Coverage of population
1832 Included householders (owner or tenant) in a property worth at least £10 p.a. (if rented) about 1 man in 7
1867 Extended franchise to lodgers paying £10 p.a. in rent about 1 man in 3
1918 All male residents over 21 about 2 men in 3
1928 Every resident or owner over 21 about 5 people in 6
The Absent Voters list for 1918 has special significance.  There was a general election in 1918, and the list was drawn up to record the 73,000 people entitled to vote who were not at home.  Nearly all these voters were on active service, and in many cases this list records their rank, service number, regiment, and of course their address. 
Electoral rolls for Birmingham are available on-line on this site, and each roll is indexed by name and address. Click here to view Birmingham, or on Search to search all the electoral rolls.