Stanley Burnton was called to the Bar in 1965. He practised initially in general common law, and then from 1976 as a commercial lawyer at One Essex Court. He took silk in 1982. He acted both as advocate and arbitrator in international arbitrations. He represented Westland Helicopters in its long-running, and ultimately successful, ICC arbitration against the Arab Organisation for Industrialisation in Geneva (the enforcement proceedings are reported at  Q.B. 282), and was the arbitrator whose appointment was unsuccessfully challenged in Laker Airways v FLS Aerospace  2 Lloyd's Law Reports 45.
Stanley Burnton sat as a deputy High Court judge in the Chancery Division from 1994 until he was appointed to the High Court Bench (Queen’s Bench Division) in July 2000. He was nominated to the Administrative Court shortly after his appointment. He was subsequently the Judge in charge of Modernisation, IT and the Court Estate and one of the original three judicial members of the Board of Her Majesty’s Court Service. He also served as a member of the Civil Justice Council.
In April 2008 he was promoted to the Court of Appeal, and sat in both the civil and criminal divisions of the Court of Appeal. He has given judgments in a number of arbitration-related cases, such as E.T.I. Euro Telecom International v Republic of Bolivia  EWCA Civ 880 (on the availability of a freezing injunction in aid of international arbitration), Itochu Corporation v Johann M.K. Blumenthal GMBH & Co  EWCA Civ 996, (a challenge to the appointment of the arbitrator), Ingosstrakh-Investments v BNP Paribas SA  EWCA Civ 644 (on the grant of an anti-suit injunction to protect a London arbitration), Broda Agro Trade (Cyprus) Limited v Alfred C. Toepfer International Gmbh  EWCA Civ 1100 (on the interpretation and effect of section 72 of the Arbitration Act 1996), and AES Ust-Kamenogorsk Hydropower Plant LLP v Ust-Kamenogorsk Hydropower Plant JSC  EWCA Civ 647,  2 Lloyd's Rep 233 (injunctive relief in aid of a London arbitration).
He retired as a Judge of the Court of Appeal on 25 October 2012, when he reached the age of 70, and has returned to One Essex Court to sit as an arbitrator. He has sat as chairman and arbitrator in a number of substantial ICC and LCIA arbitrations.
Stanley Burnton is a former chairman of the Board of Trustees of the British and Irish Legal Information Institute (BAILII). He is also a former trustee of the British Institute of International and Comparative Law, and a member of its audit committee. He is an Honorary Fellow of St Edmund Hall, Oxford.