Patients with inflammatory bowel disease (IBD) are at increased risk of colorectal cancer (CRC), and this risk increases dramatically in those who develop low-grade dysplasia (LGD). However, there is currently no accurate way to risk-stratify patients with LGD, leading to both over- and under-treatment of cancer risk. Here we show that the burden of somatic copy number alterations (CNAs) within resected LGD lesions strongly predicts future cancer development. We performed a retrospective multi-centre validated case-control study of n=122 patients (40 progressors, 82 non-progressors, 270 LGD regions). Low coverage whole genome sequencing revealed CNA burden was significantly higher in progressors than non-progressors (p=2×10-6 in discovery cohort) and was a very significant predictor of CRC risk in univariate analysis (odds ratio = 36; p=9×10-7), outperforming existing clinical risk factors such as lesion size, shape and focality. Optimal risk prediction was achieved with a multivariate model combining CNA burden with the known clinical risk factor of incomplete LGD resection. The measurement of CNAs in LGD lesions is a robust, low-cost and rapidly translatable predictor of CRC risk in IBD that can be used to direct management and so prevent CRC in high-risk individuals whilst sparing those at low-risk from unnecessary intervention.