Ollerenshaw was a product of her time, not a deliberate breaker of barriers. But she sometimes ended up flouting conventional notions of her role in society. At age eight, she went deaf. Otosclerosis, an abnormal bone growth in the middle ear, ran in her family, and an infection precipitated her deafness. She learned to read lips and went to a small school that was able to give her the attention and accommodations she needed to cope with her impairment. She believes that her deafness made mathematics an appealing subject: understanding it relied much less on hearing than other subjects did, and she benefited from good teachers who encouraged her natural mathematical curiosity. But at that time people assumed that teaching was the only appropriate mathematical career for a woman and that a deaf person could never become a teacher. The school tried to keep her out of higher math classes at age 16, but Ollerenshaw threw a fit and convinced the administration to let her continue studying math.
After graduating, Ollerenshaw gained admittance and a scholarship to Oxford, in part because her interviewers did not know she was deaf—her lipreading skill was good enough to conceal her handicap. (She had had trouble reading lips at her interview with the University of Cambridge, however, and mentioned her difficulty to an interviewer. They were much less enthusiastic about having her.) She became engaged in 1931 during her first term to childhood friend Robert Ollerenshaw, a medical student, and "envisaged a life as Robert's wife, he a practicing surgeon, myself playing the role of the supporting wife and, hopefully, mother." She wrote that her domestic ambitions and interest in sports kept her from paying as much attention to her studies as she might have. "I spent too much time playing hockey and going with Robert to dances," she wrote.
Had it not been for the interruption of everyday life by World War II, she may have continued along her planned domestic path and never fully realized her mathematical potential. The couple married hastily in 1939, just after war broke out in Europe. As she explains, "I took it for granted that Robert would be posted abroad immediately—and be slaughtered in northern France as had happened to so many soldiers. I dreaded being left unmarried after so long betrothed."
Robert was not immediately deployed, and he survived many close calls during the war. The couple had a son, Charles, in 1941, and the next year, Robert was finally sent to the field. Ollerenshaw wrote the shock was so great that she had a miscarriage. "I cried nonstop for three days and then picked myself up and took the tramcar to the university to see how I could best use my mathematics (notwithstanding being deaf) to help the war effort." She returned to earn her PhD at Oxford while tutoring "emergency" mathematics courses.
After her husband returned from the war, Ollerenshaw taught math part-time at the University of Manchester while raising their two children. (A daughter, Florence, was born in 1946.) In 1954, a few years after her first hearing aid allowed her to participate more fully in conversations, she began her political career. "To serve on the Manchester education committee seemed an ideal way of giving the public service that I had been brought up to believe should be a main objective for those not obliged to earn their own living," she wrote. Her long political career took her to the city council and numerous national education committees, including stints in Margaret Thatcher's administration in the 1980s. In 1971 she was knighted for services to education, earning the title Dame. In 1975–76 she served one term as Lord Mayor of Manchester, the "first citizen" who represented Manchester on formal and ceremonial occasions.
Ollerenshaw and her husband Robert bought a cottage 160 kilometers from Manchester just before she got involved in politics. Hodge Close was her haven, an escape from committees and duties, and the location where she performed most of her mathematics. "Every path, every steep hillside and grassy slope, every familiar rutted road has its memories of moments of insight when the solution, or at least a way forward for some problem that had been holding things up, suddenly became clear," she wrote. Mathematics was also a comfort during tragic times. In 1972 Ollerenshaw's daughter died after an 18-month battle with cancer. Her husband passed away in 1986, their son in 1999. "When I have needed solace and I have had to depend on my own resources, the mathematics has been there. I am grateful." But, as Edwards wrote, "she doesn't 'do' mathematics to escape from life. She does it because it is her greatest joy."