Isaacs, who was born in Glasgow, graduated in medicine from the university there in 1944. After three years' work in the department of bacteriology he moved to Sheffield University for a year and then spent two years in Australia at the Hall Institute for Medical Research, Melbourne. During this time he studied influenza, in particular the genetic variation of the various strains of the virus and also the response of the body to attack by the virus. He continued with this work from 1950 at the National Institute for Medical Research in London, where he was director of the World Influenza Centre.

In 1957, together with the Swiss virologist Jean Lindenmann (1924–2015), Isaacs reported that a specific low-molecular-weight protein, which interfered with the multiplication of viruses, was produced by animal cells when under viral attack. This was interferon, which he studied closely for the rest of his life, investigating problems associated with its production and isolation, its mechanism of action, and its chemical and physical properties.

In the early 1960s his health began to deteriorate but he continued work as head of the Laboratory for Research on Interferon at the National Institute.