Davies was employed by McKinsey and Company from 1982 to 1987 after working at the Treasury and the Foreign and Commonwealth Office, which included a posting of Private Secretary to the British Ambassador to France. From 1985–86 he was Special Advisor to Chancellor of the ExchequerNigel Lawson. From 1987–92 he was Controller of the Audit Commission. In 1992 he was appointed Director General of the Confederation of British Industry, a position he held until 1995, when he was appointed Deputy Governor of the Bank of England. In 1997 Davies was appointed Chairman of the newly established Financial Services Authority, serving until 2003. From 2003 to 2011 Davies served as Director of the London School of Economics and Political Science. He stepped down from the position on 3 March 2011 following concern over the institution's decision to accept funding from a foundation controlled by the Libyan dictator Muammar Gaddafi's son, Saif, and other LSE Libya Links. Davies was a non-executive director of GKN between 1989 and 1995, and a member of the International Advisory Board of NatWest Bank from 1991–95. From 1995–2004 he was founder Chairman of Employers Forum on Age, a body formed to oppose ageism at work. From 2002–10 he was a Trustee of the Tate Gallery, and was a member of the governing body of the Royal Academy of Music from 2004–13. He is Patron of Working Families, a campaigning charity which supports the rights of parents in the workplace. In 2004 he was elected to an Honorary Fellowship of Merton College, Oxford and became an independent Director of Morgan Stanley, where he chaired the Board's Risk Committee. From 2006–10, Davies served as a non-executive Director of Paternoster Ltd. Since 2003, he has held membership in the advisory board of the China Banking Regulatory Commission, and, since 2012, has chaired the Advisory Board of the China Securities Regulatory Commission. He has been chairman of the Royal Bank of Scotland since September 2015. In 2009 Davies was appointed as advisor to the Investment Strategy Committee of GIC Private Limited, formerly known as Government of Singapore Investment Corporation. Two years later he joined its International Advisory Board. He resigned from both positions in September 2012, on appointment to the chair of the Airports Commission. In 2010 he became a non-executive Director of Prudential plc, and Chair of the Risk Committee. In 2011 he joined the board of the Royal National Theatre. From 2012 to 2015 Davies was a member of the Advisory Board of the SWIFT Institute. Davies is a Council Member of the Asian Bureau of Finance and Economic Research in Singapore.
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Davies chaired the judges of the Man Booker Prize for fiction in 2007. He was appointed Chairman of the Trustees of the London Library in November 2015. He features as a character in the David Hare play The Power of Yes which premiered at the London National Theatre in October 2009.