His academic career included the founding of the Department of Drama at the University of Kent in 1970, as well as work with the British Council in Nigeria.
Bradby edited the Cambridge University Press "Studies in Modern Drama" series, as well as the journal Contemporary Theatre Review.
His 1988 book Directors’ Theatre, co-written with David Williams, had "a defining influence on younger British innovators such as Katie Mitchell and Simon McBurney.
He gave many public lectures and broadcasts and was also a consultant and advisor to many productions of works by Jean Genet, Molière, Michel Vinaver and Bernard-Marie Koltès.
[6][7] Awards named after Bradby are given out annually by the Theatre and Performance Research Association and the Standing Conference of University Drama Departments.