I think Henry was a scholar. There is no details of a wife or child, he may have been clergy. The age & DOB on the 1871 census is out, but the other details fit

1861 census
Name: Henry E F Garnsey
Age: 34
Estimated Birth Year: abt 1827
Gender: Male
Where born: Coleford, Gloucestershire, England

Civil Parish: Oxford St Peter in The East
County/Island: Oxfordshire
Country: England

1871 census
Name: Henry E F Garnsey
Age: 24
Estimated Birth Year: abt 1847
Relation: Membus Of Collige
Gender: Male
Where born: Coleford, Gloucestershire, England
Civil Parish: St Peter in The East
Ecclesiastical parish: St Peter in the East
County/Island: Oxfordshire
Country: England

1881 census
Name: H.E.F. Garnsey
Age: 54
Estimated Birth Year: abt 1827
Relation: Boarder
Gender: Male
Where born: Coleford, Gloucestershire, England

Civil Parish: Oxford St Peter in East
County/Island: Oxfordshire
Country: England

Street address: "Mag College"
Education:

Employment status:
Occupation: Fellow Mag College

Registration district: Oxford
Sub registration district: Oxford

1891 Census
E Garnsey
Age: 64
Estimated Birth Year: abt 1827
Relation: Head
Gender: Male
Where born: Glaster, Colefood

Civil Parish: St Peter in The East
Ecclesiastical parish: St Peter in the East
Town: Oxford
County/Island: Oxfordshire
Country: England

1901 census
Henry E F Garnsey
Age: 75
Estimated Birth Year: abt 1826
Gender: Male
Where born: Gloucestershire, England

Civil Parish: Bath
Ecclesiastical parish: St Swithin
Town: Bath
County/Island: Somerset
Country: England