In 1967, Craven joined SG Warburg & Co Limited, becoming an executive director in 1969. In his later career he became Group Chief Executive of White Weld & Co Ltd (subsequently Credit Suisse First Boston) from 1975 to 1978 and a vice chairman of SG Warburg & Co Limited in 1979. In 1981 he founded Phoenix Securities Limited which was acquired by Morgan Grenfell Group plc in 1987 when he took on the role of Group Chief Executive of Morgan Grenfell Group plc. He served as a member of the board of managing directors of Deutsche Bank from 1990 until 1996.
Craven was chairman of Morgan Grenfell Group plc from 1989, a post he retained when the group was renamed as Deutsche Morgan Grenfell Group plc in 1996. He is a non-executive director of Rothmans International plc and a member of the Supervisory Board, Société Générale de Surveillance SA, Geneva. He is also a Trustee of the Cambridge University Foundation.