Professor Crossick is Vice-Chancellor, University of London, having previously been Warden of Goldsmiths (2005-10).

As Chief Executive of the Arts and Humanities Research Board (2002- 2005), he took it through to its establishment as a full research council.

Professor Crossick is a member of the Board of Universities UK and its Policy Networks for both Research and Funding, as well as being a member of the HEFCE Enterprise and Skills Committee. He is Chair of the university sector’s Financial Sustainability Strategy Group. His essay 'The Future Is More Than Just Tomorrow: Higher Education, The Economy And The Longer Term' was published by Universities UK in September 2010.

Professor Crossick is active in debates about the importance of the arts and humanities, including the creative industries. He is a social historian specialising in the urban social history of 19th and 20th century Britain and continental Europe.

A Fellow of both the Royal Historical Society and the Royal Society of Arts, Professor Crossick was in 2004 elected an Honorary Fellow of Emmanuel College, Cambridge.