Edwin's younger brother Francis Turner/James appears to have stayed in the Birmingam area. I have found him on 1871 and 1881 as Franci(e)s Osbaldeston, married to Sarah. On 1871 he is a basket maker and 1881 a beer house keeper. So the whole family are missing on 1861, wonder where they were?
Just checked Francis married Sarah Reeves in 1869 in Birmingham.
IGI 25 Dec 1869 St Thomas Birmingham Francis Osboldiston to Sarah Reeves.