 After graduating from Oxford, Goldman trained in (and later taught) haematology and oncology at several medical schools and hospitals, including St. Bartholomew's Hospital, Harvard University, and the University of Miami.In 1971 Goldman joined the staff of Hammersmith Hospital, London, and became a specialist in the treatment of chronic myeloid leukaemia.During the 1980s, he conducted some of the first bone marrow transplants in Europe, and also developed precise molecular tests to detect residual leukaemia cells in the blood of patients.