Not to throw a spanner in the works but how certain is it that Nehemiah was William's father?
On the 1911 census William lists the streets where all his family were born and for William himself it was Clifton Road, Aston. Nehemiah's son William's birth was registered in Bham not Aston which in itself is not a deal breaker.
However, on William's (Nehemiah's son) baptism his dob is listed as 20 Jun 1879 whilst on William's (Agnes Louisa's husband) RAF record his dob is listed as 27 May 1879.
Possibly making him the son of a Thomas Johnson and a Matilda Wainwright.