Name: BARNARD, BENJAMIN FREDERICK
Initials: B F
Nationality: United Kingdom
Regiment/Service: Royal Flying Corps
Unit Text: 8th Sqdn.
Date of Death: 15/08/1915
Service No: 1483
Additional information: Son of Benjamin and Janet Barnard.
Casualty Type: Commonwealth War Dead
Grave/Memorial Reference: Plot 1. Row C. Grave 1.
Cemetery: LOUVENCOURT MILITARY CEMETERY
I know that going backwards wasn't what you asked for, but at least it gives you somewhere to start looking...
1891 census info from ancestry.com:
He was born Q3 1889
Name: Benjamin F Barnard
Father's Name: Benjamin
Mother's Name: Janet
Where born: Shoreditch, London, England
Father was a wool sorter, mother was a boxmaker. They lived at 79 Nicholas Street in Shoreditch.
Household Members: Name Age
Benjamin Barnard 23
Benjamin F Barnard 1
Janet Barnard 23
Janet E Barnard 3/1
By 1901 they were in 3, Hols Place in Shoreditch, with a lot more children.
I don't know the history of Shoreditch at all. With a name like Benjamin in the family, they may have been Jewish, which may help your search for descendants. Brother Bertie (b. c. 1903) may have served, too, which might give you a later angle to go at.
Other than that, going forward in time is pretty difficult. You might start a family tree with these people in genes reunited, and see if anyone else has these names in their tree.
Best of luck.