I can only find one William and Elizabeth Jenney living in Brum on the 1881 census, dosent fit the DOB or POB though.
Dwelling: 6 Saltley Road South Side
Census Place: Aston, Warwick, England
Source: FHL Film 1341724 PRO Ref RG11 Piece 3032 Folio 47 Page 15
Marr Age Sex Birthplace
William JENNEY M 44 M Birmingham, Warwick, England
Rel: Head
Occ: Marine Store Dealer
Eliza B. JENNEY M 37 F Aston, Warwick, England
Rel: Wife
Harry B. JENNEY 7 M Birmingham, Warwick, England
Rel: Son
Occ: Scholar
Frederick C. JENNEY 5 M Aston, Warwick, England
Rel: Son
Occ: Scholar
Lilian K. JENNEY 3 F Birmingham, Warwick, England
Rel: Daur
Sydney N. JENNEY 10 m M Birmingham, Warwick, England
Rel: Son
Matilda M. BURTIN 14 F Birmingham, Warwick, England
Rel: Serv
Occ: (Dom)