Stallard read mathematics at
King's College, Cambridge, finishing in 1985, and earned her Ph.D. from
Imperial College London in 1991. Her dissertation,
Some problems in the iteration of meromorphic functions, was supervised by Irvine Noel Baker. She has spoken about the difficulty of finding postdoctoral research positions at a time when there were few such positions in England and the ties of her husband's job prevented her from moving abroad; she maintained her mathematical career at this stage by taking a temporary lectureship teaching engineering students at the
University of Southampton. When she became a professor of mathematics at the Open University, she became the first woman to be a professor in the department. ==Activism and recognition==