Is this the Francis Edward Grainger you are looking for?
1901 England Census
about Francis E Grainger
Age: 13
Estimated Birth Year: abt 1888
Relation: Son
Father's Name: Francis W
Mother's Name: Alice
Gender: Male
Where born: Birmingham, Warwickshire, England
Civil parish: Aston Manor
Ecclesiastical parish: Lozells St Paul
County/Island: Warwickshire Country: England
Street Address: 22 Kensington Street
Registration district: Aston Sub-registration district: Aston Manor
ED, institution, or vessel: 21 Household schedule number: 47
Household Members:
Francis W Grainger 33 (born Wolverhampton-tin plate worker)
Alice Grainger 33 (born B'ham-nurse on own account)
all children born B'ham
Francis E Grainger 13 (jewellery trade worker)
Gertie E Grainger 12
Bertie E Grainger 11
Florrie A Grainger 8
Arthur J Grainger 4
Leonard Facer 19 (brother-packer at printers) (presumably Alice's brother?)
Possible birth cert details
Name: Francis Edward Grainger
Year of Registration: 1887 Quarter of Registration: Jul-Aug-Sep
District: Birmingham (1837-1924) County: Warwickshire
Volume: 6d Page: 107
Marriage cert details
Name: Francis E Grainger
Year of Registration: 1915 Quarter of Registration: Oct-Nov-Dec
Spouse's Surname: Buxton
District: Aston (1837-1924) County: Warwickshire
Volume: 6d Page: 1542
Parents' marriage cert details
Name: Alice Facer
Year of Registration: 1886 Quarter of Registration: Apr-May-Jun
District: Aston (1837-1924) County: Warwickshire
Volume: 6d Page: 549