This compared to just eight cases per 10,000 women among those with an adequate screening history and normal results.
Meanwhile, women who had been screened regularly but had an abnormal result between the ages of 50 and 64 had the highest risk of all - 86 cervical cancer cases per 10,000 women at age 65 to 83.
The researchers said the level of protection offered by a good screening history of normal results does fall over time, but can last well into the 80s.
Professor Peter Sasieni, Cancer Research UK's expert on cervical screening and co-author of the study, from Queen Mary University of London, said: "With life expectancy increasing, it's important for countries that stop screening under age 60 to look into their screening programmes to maximise the number of cervical cancer cases prevented and the number of cervical cancers caught at an early stage."
Jessica Kirby, Cancer Research UK's senior health information manager, said: "Screening can pick up abnormal cells in the cervix that could develop into cervical cancer if left alone - removing these cells prevents cancer from developing. Screening is a great way of reducing the risk of cervical cancer, and saves up to 5000 lives a year in the UK."
- PAA