Epstein, a Londoner, was educated at Cambridge University and at the Middlesex Hospital Medical School in his native city. After serving in the Royal Army Medical Corps (1945–47), he returned to the Middlesex Hospital as an assistant pathologist. He left the Middlesex in 1965 and in 1968 he was appointed professor of pathology at Bristol University, a position he held until his retirement in 1985. He has continued to work in the Department of Clinical Medicine at Oxford.

In 1961 Epstein heard Denis Burkitt describe the distribution of a particularly savage lymphoma throughout Africa. Epstein saw that “anything which has geographical factors such as climate affecting distribution must have some kind of biological cause.” That biological cause, Epstein suspected, for no very good reason, was a virus.

Although Epstein received tumor samples from Burkitt, he found them impossible to culture and saw no trace of any virus. After struggling unsuccessfully for two years, Epstein and his assistant Yvonne Barr developed a new approach. Instead of working with small tumor lumps they divided the pieces into single cells. The technique proved successful and for the first time ever human lymphocytes were being grown in a continuous culture.

Yet Epstein initially found no virus until he examined some cells under an electron microscope. The virus was named the Epstein–Barr virus and proved to be a member of the herpes family.

The virus turned out to have a worldwide distribution and was identified as the cause of mononeucleosis. Clearly, its presence alone is insufficient to cause lymphoma. For if most of us have the virus, why is lymphoma not distributed more widely? Epstein and Burkitt argued that only in cases in which malaria or some other chronic condition has suppressed a child's immature immune system, could the virus provoke lymphoid cells into malignant growth.