Professor Feldman graduated in 1975 with a first-class honours B.A. in Jurisprudence from Exeter College, University of Oxford where he also received his first-class honours B.C.L. and D.C.L.

He was a Lecturer in Law from 1976 to 1989 and Reader in Law from 1989 to 1992 at the University of Bristol. From 1992 to 2004, he was Barber Professor of Jurisprudence and Professor of Law at the University of Birmingham (concurrently holding the positions of Dean of the Faculty and Head of the School of Law 1997-2000). From 2000 to 2004, he was Legal Adviser to the Parliamentary Joint Select Committee on Human Rights, Houses of Parliament of the United Kingdom. From 2003, he was Fellow of Downing College, Cambridge and as of 2004 Rouse Ball Professor of English Law, University of Cambridge.  He became the Chairman of the Faculty Board of Law in 2006. He was also Academic Associate of Chambers, 39 Essex Street, London since 2004.  He was also elected to the British Academy in 2006. He was also a Visiting Fellow, Faculty of Law, Australian National University (1989) and Distinguished Visiting Fellow at the University of Melbourne (2006).

He has authored many journal articles and contributed to edited volumes on comparative public law, human rights, constitutional and administrative law, constitutional theory, criminal procedure, the law of public and private law remedies, and professional regulation. He is also the author of the books: The Law relating to Entry, Search and Seizure (London: Butterworths, 1986) Criminal Confiscation Orders: the New Law (London: Butterworths, 1988) Civil Liberties and Human Rights in England and Wales (Oxford: Clarendon Press, 1993; 2nd edition, Oxford University Press, 2002) (ed.), English Public Law (Oxford: Oxford University Press, 2004).

He served as a Judge of the Constitutional Court of Bosnia and Herzegovina from July 2002 to January 2011. He served as the Vice-President from 2006 to 2009.