Normington was appointed a Companion of the Order of the Bath (CB) in the 2000 New Year Honours, promoted to Knight Commander of the same Order (KCB) in the 2005 New Year Honours, and promoted again to Knight Grand Cross of that Order (GCB) in the 2011 New Year Honours. In 2010 it was announced that he would retire from the Civil Service and become the First Civil Service Commissioner and Commissioner for Public Appointments, the first time the two roles had been combined.