She was elected a Fellow of the Academy of Medical Sciences in 2000, and was the first British researcher to be awarded the American Society of Hematology Henry M. Stratton Medal.
Stevenson became interested in cancer immunology: the use of Immunoglobulin (antibodies) to attack cancer cells. She focussed on a receptor of leukaemic B lymphocytes: a leukaemia-specific protein. By developing an antibody against this protein, which was one of the first demonstrations of cancer immunology in research. She was the first to demonstrate that anti-CD28, a monoclonal antibody that binds to the CD38 protein, could be used to treat several types of myeloma. anti-CD28, now named theralizumab was developed in Stevenson's laboratory, and is now the normal treatment pathway for patients with bone marrow cancer.