Murray was editor of Building Design and then the RIBA Journal. In 1983, he launched Blueprint magazine with Deyan Sudjic; this was followed by Eye, the international review of graphic design and Tate magazine for the Tate Gallery. He has worked on major projects around the world including Broadgate in the UK, Taipei 101, Taiwan, Union Square in Hong Kong, Avant Seine in Paris and Hudson Yards and One World Trade Center in New York City. In 2004, Murray launched the first London Architecture Biennale (now the London Festival of Architecture) in Clerkenwell.
He is chairman of New London Architecture: the centre for London's built environment and President of Wordsearch, a consultancy explaining and promoting architecture, planning and the built environment.
A prolific author, his works include The Saga of Sydney Opera House, "A passion to build" and "Architecture and Commerce."
Murray was made a fellow of the Royal Society of Arts in 1989 and an Honorary Fellow of the Royal Institute of British Architects in 1999. He is a member of the Academy of Urbanism, a board member of the Center for Active Design and of the Association of Architectural Organisations.
Murray was appointed Officer of the Order of the British Empire (OBE) in the 2021 Birthday Honours for services to leadership in the arts, architecture, city planning, design and publication and to charity.[3]