Damian was first elected to Parliament 1997, being re-elected seven times, most recently in 2019.

He was the First Secretary of State and Minister for the Cabinet Office from June 2017 until December 2017.

In 2016 he was the Secretary of State for Work and Pensions, and from 2012-14 was Minister of State for Policing, Criminal Justice and Victims, a role covering both the Home Office and the Ministry of Justice. In October 2012 he was made a member of the Privy Council. From May 2010 to October 2012 he was Minister of State for Immigration.

He was a Conservative Spokesman on Education and Employment from 1998-99, Conservative Environment Spokesman from 1999-2001, Shadow Secretary of State for Education and Skills from 2001-2003, and Shadow Secretary of State for Transport from 2003-2004. From July 2004-2005 he was a member of the Home Affairs Select Committee; from July to December 2005 he was a member of the Treasury Select Committee. 

In December 2005, he was appointed Shadow Minister for Immigration.

He is a former financial journalist and worked in the Prime Minister's Policy Unit from 1992-94. Damian contested Brent East in the 1992 General Election. He was educated at Reading School and Balliol College, Oxford. He was President of the Oxford Union in 1977. He is married with two daughters.