Sir Martin Moore-Bick attended The Skinners' grammar school in Tunbridge Wells, followed by Christ's College, Cambridge. He was called to the Bar by Inner Temple in 1969, and joined 3 Essex Court (now 20 Essex Street), where he specialised in insurance and reinsurance, shipping, and the international sale of goods. He was appointed Queen’s Counsel in 1986, and was a Recorder from 1990 to 1995. He also sat as a commercial arbitrator while at the Bar. He was made a Queen's Bench Judge in 1995. He was nominated to sit in the Commercial Court, and was the Judge In Charge from 2000 to 2002. He became a Lord Justice of Appeal in 2005, and was Deputy Head of Civil Justice from 2007 to 2012 and Vice-President of the Court of Appeal (Civil Division) from 2014 to 2016. Shortly after retiring from the Bench and resuming his practice as an arbitrator, he was appointed Chair of the Public Inquiry into the Grenfell Tower Fire.

Sir Martin’s pastimes include reading and early music, and he is also a keen gardener.