Connor was born on 11 February 1955 in Chichester or Bognor Regis, both in Sussex, England. From 1966 to 1972, he was educated at Christ's Hospital, then an all-boys independent school in Horsham, Sussex. Having been expelled from Christ's Hospital, he attended Bognor Regis School, a comprehensive school in Bognor Regis. In 1973, he matriculated into Wadham College, Oxford to study English; his tutor was Terry Eagleton. He graduated with a first class Bachelor of Arts (BA) degree in 1976. He remained at Oxford to study for a Doctor of Philosophy (DPhil) degree in English. He completed his doctorate in 1980 with a thesis titled "Prose fantasy and myth-criticism 1880–1900".
In 1979 or 1980, Connor joined Birkbeck College, University of London, as a lecturer in English. He was promoted to senior lecturer in 1990, made Reader in Modern English Literature in 1991, and appointed Professor of Modern Literature and Theory in 1994. He held two senior positions at the college: he was Pro-Vice-Master for International and Research Students between 1998 and 2001; and College Orator between 2001 and 2012. From 2002 to 2012, he additionally served as Academic Director of the London Consortium, an graduate school of the University of London that specialised multidisciplinary programs.
In 1984, Connor married Lindsey Richardson. Together they had one daughter. They divorced in 1988. In 2005, Connor married Lynda Nead. Together they have two sons. Nead is an art Historian and academic.
In 2012, Connor was elected an Honorary Fellow of Birkbeck, University of London. In July 2016, he was elected a Fellow of the British Academy (FBA), the United Kingdom's national academy for the humanities and social sciences.
