There does seem to be a hit for a William Gifkins, but not for, say, Sarah or Martin so probably either unrelated or something to do with William Jr.
From the 1871 census, I can see them scattered, possibly:
Catherine, 45, b. Gilbraltrar, a widow and servant in St. Michael Winchester Hampshire
Mary, 23, b. Ireland, a ladies maid in Marylebone
Sarah, 22, b. India, schoolmistress, brother Charlie, 11, b. Winchester Hampshire and sister Catherine, 9, b. Winchester Hampshire, in St. Thomas Winchester
Martin, 14, b. Meerat India, at Woolhampton College St. Mary in Berkshire.
In 1861 I found them misindexed (as "Pipkins" on what I have, don't know about what Ancestry will list them under. Handwriting is not the easiest)
RG9/691 folio 118 page 14
Clement Street, St. Thomas Winchester
William Jifkins? (old-style f looks like a p, first letter of surname hard to read), 39 (or possibly 37), soldier, b. Oxfordshire Chatgray(??)
Catherine, 32, b. Ireland
Mary M, 16, b. Ireland
Sarah, 14, b. East Indies
William, 12, b. East Indies
Martin, 5, b. East Indies
Henry, 3, b. East Indies
Charles, 1, b. Hants Winchester