Cervical cancer screening is a life-saving endeavour. The introduction of an organized population-based national screening programmes has potential to both reduce incidence of cervical cancer in an asymptomatic population and detect early-stage cancers for accelerated treatment. A methodology for estimating cancers prevented by such programmes has immediate utility. This work derives a model for estimating cancer prevented by screening, applied to data from Ireland’s organized national cervical screening programme since its introduction in August 2008 to August 2022. A novel Markov-chain model for human papilloma virus (HPV) induced cervical cancer was derived with realistic transition probabilities validated against literature estimates. Data from the Irish National Screening Programme (CervicalCheck) and from the National Cancer Registry of Ireland (NCRI) was applied to estimate the number of cancers prevented by screening, changes in Irish cancer detection since the implementation of screening, and treatment costs saved by screening. Since its inception in 2008, the modelling in this work suggests that CervicalCheck has prevented an estimated 5557 cancers (95% confidence interval: 5114–6000 cancers) and saved €102 million in future treatment costs (95% confidence interval: €94–110 million) not including inflation costs. Additionally, 48.8% (95% confidence interval: 41.4%–56.2%) of all cervical cancers in Ireland have been detected through screening between 2008 and 2022. National screening in Ireland has been highly effective at reducing future cervical cancers, and detecting asymptomatic cancers. The model outlined here has direct future applicability for the assessment of national and regional cervical cancer screening programmes.