I have found the following information about your CORDY family in the 1871 UK English Census (all born in Norfolk - Parents in Holme Hale [5.5 miles from Swaffham] and the children in Beechamwell):
Beechamwell Street, Beechamwell [5 miles from Swaffham)
Cornelius 42, Head, Labourer, Sarah 42, Wife, Susannah 16, Daughter, Rosena 14, Daughter, Jonas 12, Son, "Shephud Boy" (sic), Mary 10, Daughter, Margaret 8, Daughter, Sarah 6, Daughter, William 4, Son, Robert SECKER 37, Lodger, "Shephud" (sic).
Cornelius appears to have been Baptised in Holme Hale on 15 February 1829 and his father was also called Cornelius.
1841 Census shows Cornelius living with his parents in Holme Hale: