After receiving several undergraduate prizes, Professor Greaves graduated MB BS from the University of London. Subsequently he obtained the membership of the Royal College of Physicians, was elected a Fellow in 1974 and graduated MD (London). Professor Greaves was a graduate student and UK Medical Research Council Fellow for 3 years at University College London where he proceeded to a PhD (pharmacology) (Faculty of Medicine) by thesis. His dermatological training was at St. John's Institute of Dermatology, London and the Royal Victoria Infirmary, University of Newcastle-upon-Tyne.
Professor Greaves was appointed Clinical Professor and Head at St. John's Institute of Dermatology in 1975, and subsequently Dean of the Institute. Following his retirement, and at the request of the Persatuan Dermatologi Malaysia, he was appointed Clinical Professor (Dermatology) at the University Kebangsaan Malaysia in 2001 with the remit of establishing a specialist training course in Dermatology for Malaysia. This course is flourishing at the present time.
In 2003 Professor Greaves re-located to Singapore, initially at Singapore General Hospital and later at the National Skin Centre Singapore with the title of Clinical Professor, National University of Singapore and was elected Fellow of the Academy of Medicine of Singapore. During this period he carried out original research on the clinical, histopathological and immunopathological manifestations of the skin in dengue haemorrhagic fever. He was, at Singapore General Hospital, deeply involved in coping with SARS (severe acute respiratory syndrome) which claimed many Singaporean lives (vide Greaves MW. Coping with SARS: a day in the life of a UK Dermatologist in Singapore General Hospital J Amer Acad Dermatol. Vol 50, March 2004).
He and his wife narrowly escaped death due to the Dec 26th 2004 tsunami whilst vacationing in Dusit Laguna resort, Phuket (vide Greaves MW. Killer waves at yuletide: a hair-raising experience. J Amer Acad Dermatol. Vol 52 Special Article. June 2005)
Since returning to the UK in 2007, Professor Greaves has worked as an NHS consultant in the Cutaneous Allergy Clinic at St. John's Institute of Dermatology, St. Thomas' Hospital, and as a specialist in dermatology and dermatological allergy here, at the London Allergy Clinic.