His career has included a focus on the role of spinal cord circuits in the control of movement,[6] the excitability of peripheral nerve axons in health and disease, and other areas of clinical neurophysiology.
[9] Burke was inspired to undertake medical research and then to pursue a career in neurology by Professor James W. Lance, AO, CBE,[10] and studied at The Prince Henry Hospital under his guidance.
[11] After completing the MD by research, he became a medical registrar at Prince Henry, and passed the examinations of the Royal Australasian College of Physicians (awarded MRACP in 1972 and FRACP in 1975).
[3] In 1980, he was appointed Staff Specialist Neurologist at Prince Henry and Associate Professor (conjoint) with the University of New South Wales.
[3] His personal research, in particular that with Professor Simon Gandevia involved microneurography and other motor control studies on human subjects.
[21] In the 2019 Queen's Birthday Honours, Burke was made a Companion of the Order of Australia (AC) "for eminent service to neurophysiology, to innovative treatments for spinal cord and brain trauma injuries, and to professional medical organisations".