Born in Britain, Oatley graduated from Loughborough University in 1976 with an Automotive Engineering degree. He worked briefly outside motor racing before joining the Williams team in 1977. There he became one of many young engineers to have worked alongside Patrick Head early in their careers before moving on to other organisations. Oatley worked as a draughtsman before becoming a race engineer for both Clay Regazzoni and Carlos Reutemann.
Oatley joined the McLaren team shortly after leaving FORCE and worked alongside John Barnard in the design office. Barnard was soon replaced by Gordon Murray whose MP4/4 chassis almost completed a clean sweep of victories in 1988, and when Murray moved to the new McLaren road car project Neil Oatley was made Chief Designer, his cars securing titles in 1989, 1990, 1991, 1998 and 1999.
Oatley continued to work as Chief Designer at McLaren until 2003 when he became Executive Director of Engineering.