This looks like the FERREY family in 1861 - mistranscribed on the index I have as
Terrey. - enumerator's handwriting is not always easy to read!
1861 at 5 Union St, Southampton St Mary
William Ferrey 40, seaman, b Southampton
Caroline Ferrey 37, b Lymington
Charles Ferrey 11,, b Southampton
Caroline Ferrey 9, b Southampton
Mary J Ferrey 5, b Southampton
John Ferrey 3, b Southampton
Alice Ferrey 1, b Southampton
1871, listed as Ferry
at Cook St, Southampton St Mary.
All other information is the same, except that John has an occupation - mariner, and William is also 'mariner'
William Ferry 56
Caroline Ferry 47Mary J Ferry 16
John Ferry 14
Alice Ferry 12
Henry Ferry 10
1881 at 10 Duke St, Southampton St Mary
Caroline FERRY, widow, age 56, place of birth given as Milford. there are two lodgers with her - Jane and Frederick DOLE
1891 at 27 Duke St, Southampton St Mary
Caroline FERRY 67, b Lymington
Hilda Pickering 11, granddaughter, b Southampton
Alice Pickering 8, granddaughter, b Southampton
FreeBMD shows these deaths, although the age is not right for William (ages given on census are a bit flaky though) and a couple of years out for Caroline

Dec qr
1873
William FERRY 52, death reg at Southampton Vol 2c, page 6
Mar qr
1900
Caroline FERRY 74, death reg Southampton, Vol 2c page 34
Stephen: FreeBMD has some deaths registered in Christchurch for FERREY
Judith