The Nutley names can be derived from different original names, so caution is urged.
I have been studying the Notley family of Ireland. In proven ancestries, the surname can become Notley, notly, notely, noteley. Also Nutley, nutly etc. So some Nutley/nutly families might be derived from Notley and its variants.
Alternatively there were some nutleys that arrived directly from England. For example Richard Nutley, one of Queen Anne's Irish judges.