Well the deer link could be wrong. My dad was told it when he was doing some half-hearted geneology some years back: of the "send us a tenner and we'll send you a scroll with your family history on it" variety. Could be that the company couldn't find a derivation of Deards and picked the nearest!
We came from the same area. My grandparents left the Cambridge/Norfolk area around the 1950s to move to first London and then Oxford, finally settling in Littlehampton. My family is now based in Reading.