Bernard Henry GIDNEY would appear to be Mortimer's brother - here's the 1871 census entry for Charles and Hannah GIDNEY and family. (The surname looks like GEDNEY on the original image.)
RG10/559/79/33 - 3 Lukes Place, Mile End Old Town
Charles GIDNEY - Head - 41 - Ham & Beef Dealer - Bow
Hannah GIDNEY - Wife - 40 - Islington
Bernard H GIDNEY - Son - 15 - Office Lad - Hampstead
Florence A GIDNEY - Dau - 14 - Hampstead
Annie GIDNEY - Dau - 12 - Scholar - Hampstead
Charles H GIDNEY - Son - 11 - Office Lad - Islington
Mortimer C GIDNEY - Son - 8 - Scholar - Islington
Emily GIDNEY - Dau - 7 - Scholar - City of London
Kate GIDNEY - Dau - 6 - Scholar - Hoxton
Walter GIDNEY - Son - 5 - Hoxton
Nelly GIDNEY - Dau - 4 - Stepney
Clara GIDNEY - Dau - 3 - Stepney
Arthur GIDNEY - Son - 1 - Stepney
Rambler