I do not know if you have seen the 1911 census. This has John, his wife Sarah and daughter Lilian at back of 38 Hunters Vale, and john as a groom carter for a wine merchants . John moved after that.
I think there is some confusion. This includes in Kellys directories. There is a Kerby road in Erdington, off Marsh Hill . there is a Kirby road in Winson Green. Kellys directories in their list of streets in Birmingham also lists a Kirby Road off Marsh Lane, but does not include it in their section on streets in which individual properties are listed (this is not entirely unusual for a short road which has only residences and no firms in it). I can find no mention of a Kirby road in Erdington other than the one previously stated, and believe this was an error. In any case John Smart is listed at 7 Kerby Road in the electoral rolls for 1918 (when he is absent in the army listed as 3051UF, Pte, 16th Batt, RWR ) and 1919 (again in army as 305117, Pte., 16th Batt., R.W.R. B.E.F., France ), and remains there till at least 1930, though is not there in 1935 (online electoral rolls do not give every year). Lilian, as a woman would not be included till she was 21 if she was still there., but is not listed there at all, In 1920 -1930 Jane smart is listed at that address, and in 1920 Victor wild is listed there. In 1927 william Andrews is listed there (I add these two in case the names mean anything to you, though they might just be lodgers). A map from c 1963 below shows where no 7 Kerby Road was.
There are several other Lilian smarts on the electoral roll, so cannot determine which is her, assuming she was even still in the Birmingham electoral district
