I have been collecting references to the names ELWICK and ELLWICK since 1989 and hope my collection will help you. According to "A Dictionary of English Surnames" by P.H.Reaney & R.M.Wilson the name is thought to derive from a village of the same name but there are 2 one in Durham and the other in Northumberland. The 1585 Visitation of Yorkshire mentions ELWICK's of Elwick Tower Northumberland but the name is found in Nottinghamshire, Yorkshire and London throughout the 16th century.
I am registered with the Guild of One-Name Studies and thereby answer all queries relating to the names ELWICK, ELLWICK and HELWICK.
Site updated 5 Feb 2015