He has carried out extensive research on racism and mental illness and is the first black consultant psychiatrist appointed by Britain's National Health Service (NHS).

[4] That year, the political activist and academic Walter Rodney noted in his memoirs, that Burke was posted at the University Hospital, Mona, Jamaica.

[10][11] He reported that 20 per cent had been sent from the high-security psychiatric unit Broadmoor Hospital, the majority had not wished to return to Jamaica and most were diagnosed with paranoia, despite Burke noting that they lacked any delusions with regards to discrimination based on skin colour.

[11][12] Burke calculated that one in four would die, and concluded that repatriation was a "gross social insult", caused significant psychological harm and had no therapeutic benefit.

[33] When treating West Indian people with mental illness, he used his familiarity with key Jamaican role models including Marcus Garvey, Bob Marley and the Rastafarian movement.

[28] He wrote on the limitations of one-to-one counselling in Afro-Caribbean people with mental illness when a significant contributory factor to their condition was family stress, and that a positive outcome was strongly influenced by the family-patient interaction.

[1][40] The Commission for Racial Equality (CRE) was subsequently made aware that software used for medical-school admissions selection at St George's was creating a lower score for women and those with non-European names, so reducing their chance of being called for interview.

[39][41] Following an enquiry, the official CRE report (1988) confirmed Burke and Collier's findings and also questioned what might be happening in other London medical schools; St. George's already had a higher than average intake of students with non-European names.

[45] In the Prins Inquiry, Burke suggested that Orville Blackwood "was a man with profound insight" and termed his illness as "acute stress-related psychotic disorder".

[37] He remained at St George's until his retirement, following which he continues with work in psychiatry, writing on black mental health issues and assisting the General Medical Council.

[4] In February 2010 he was the keynote speaker at the 5th Annual Huntley Conference, which was on the theme "Young, Black and British: Identity and Community through the generations" and was held at London Metropolitan Archives, where he explained how the supplementary school movement gave new immigrants a sense of being Caribbean.

[48] Burke's other roles have included being the president of the Transcultural Psychiatry Society (TCPS), which focused on issues of culture and race in British mental health services.

[51] He was also appointed the vice-chair and a trustee of the George Padmore Institute,[52][53] an archive, educational, research and information centre that was founded in 1991 by John La Rose together with a group of political and cultural activists connected to New Beacon Books.

[60] On 6 April 2022, Burke delivered the annual Lord Pitt Memorial Lecture, organised by the British Caribbean Association and held at the UCL Institute of Education.

[6] Their father Revd Eddie Burke, who died on 3 July 2000 at the age of 91, was described in the Newsletter of the George Padmore Institute as a "a leading figure in the modern history of Jamaica".