From 1838 Josiah Cox Woodhill, factor, occupied 26 Frederick st with his wife & children .No leaving date. The house (not now of course a house) is still there and listed in “The Birmingham Jewellery Quarter” John Catell et al
The land tax records (Ancestry) show a J Woodhill as being the owner & occupier of a building in Dale End in 1825 and 1829.
Looking at directories :
Before 1829 there is no mention of Josiah, though John Woodhill & son are factors and jeweller
1833 Woodhill James and J. C. factors, 19 Vittoria-st.
1839 Woodhill James, fsctor 19 Vittoria-st
1841 Woodhill Josiah Cox, factor, 26 Frederick st
1849 Woodhjll Josiah Cox, jeweller, 20 Vittoria street
They show him living at
1829 Woodhill Josiah, Regent'e-place (assuming it is same Josiah)
1845-49 Woodhill Josiah Cox, gentleman, 20, Vittoria st
1852 Woodhill Josiah 30 Calthorpe St
1855-1882 Woodhill Josiah Cox 20 Charlotte road.
From 1883 it is occupied by Mrs Woodhill
Have just seen Polly's post also