Background Women genetically predisposed to breast cancer often develop the disease at a young age when dense breast tissue reduces the sensitivity of X-ray mammography. Our aim was, therefore, to compare contrast enhanced magnetic resonance imaging (CE MRI) with mammography for screening. Methods We did a prospective multicentre cohort study in 649 women aged 35–49 years with a strong family history of breast cancer or a high probability of a BRCA1, BRCA2, or TP53 mutation. We recruited participants from 22 centres in the UK, and offered the women annual screening with CE MRI and mammography for 2–7 years. Findings We diagnosed 35 cancers in the 649 women screened with both mammography and CE MRI (1881 screens): 19 by CE MRI only, six by mammography only, and eight by both, with two interval cases. Sensitivity was significantly higher for CE MRI (77%, 95% CI 60–90) than for mammography (40%, 24–58; p=0·01), and was 94% (81–99) when both methods were used. Specificity was 93% (92–95) for mammography, 81% (80–83) for CE MRI (p<0·0001), and 77% (75–79) with both methods. The difference between CE MRI and mammography sensitivities was particularly pronounced in BRCA1 carriers (13 cancers; 92% vs 23%, p=0·004). Interpretation Our findings indicate that CE MRI is more sensitive than mammography for cancer detection. Specificity for both procedures was acceptable. Despite a high proportion of grade 3 cancers, tumours were small and few women were node positive. Annual screening, combining CE MRI and mammography, would detect most tumours in this risk group.