Until January 2011 Burton was Chairman of the High Court Judges Association and served as Treasurer of Gray's Inn in 2012.
He was appointed Knight Grand Cross of the Order of the British Empire (GBE) in the 2019 Birthday Honours.
[11] Burton is the figurehead of the Investigatory Powers Tribunal since its inception in 2000 and has played a pivotal role in the UK's world-leading oversight of its security and intelligence agencies.
The trust has funded art therapy for cancer patients as well as providing support for students wanting to pursue this field.
Most notably, he has set up a scholarship fund at Goldsmiths College, London University which is awarded every year to a student who wishes to study art psychotherapy with a focus on cancer care.