He was brought up in Hampstead Garden Suburb and studied at Leighton Park School in Reading and then at Street Peter"s College, Oxford.
Gavron became a barrister and was called to the bar by Middle Temple in 1955. Gavron founded the Street Ives Group in 1964, serving as chairman from 1964 to 1993. He was the director of Octopus Publishing between 1975 and 1987 and Electra Management from 1981 to 1992.
He was also the proprietor of the Carcanet Press from 1983 to 2015 and served as the chairman of the Folio Society, (1982-2015) and the National Gallery Company Limited (1996-1998).
He was both chairman of the Guardian Media Group and a trustee of the Scott Trust between 1997 and 2000. Gavron was chairman of the Open College of the Arts (1991-1996), a director of the Royal Opera House (1992-1998), a trustee of the National Gallery (1994-2001), and of the Paul Hamlyn Foundation (1987-2005).
He was a governor of the London School of Economics (1997-2002) and chaired his own charitable trust, the Robert Gavron Charitable Trust (1974-2015). He was in 1996 elected an Honorary Fellow of the Royal Society of Literature.
Gavron was active in the Labour Party and a financial contributor to the Labour Leader" General’ s Office Fund, run by Lord Levy, which financed Tony Blair"s private office before the 1997 General Election.
He was appointed a Commander of the British Empire (Commander of the Order of the British Empire) in the 1990 Birthday Honours, and received a life peerage as Baron Gavron, of Highgate in the Borough of Camden, on 6 August 1999. Gavron served on House of Lords, United Kingdom Parliament, Works of Art Committee from 1999 – 2003 and 2005 – 2009.
Gavron was a member of the Groucho and the Master Control Console.