Familial hypercholesterolaemia (FH) is a common inherited disorder, causing lifelong elevated low-density lipoprotein cholesterol (LDL-C). Most individuals with FH remain undiagnosed, precluding opportunities to prevent premature heart disease and death. Some machine-learning approaches improve detection of FH in electronic health records, though clinical impact is under-explored. We assessed performance of an array of machine-learning approaches for enhancing detection of FH, and their clinical utility, within a large primary care population. A retrospective cohort study was done using routine primary care clinical records of 4,027,775 individuals from the United Kingdom with total cholesterol measured from 1 January 1999 to 25 June 2019. Predictive accuracy of five common machine-learning algorithms (logistic regression, random forest, gradient boosting machines, neural networks and ensemble learning) were assessed for detecting FH. Predictive accuracy was assessed by area under the receiver operating curves (AUC) and expected vs observed calibration slope; with clinical utility assessed by expected case-review workload and likelihood ratios. There were 7928 incident diagnoses of FH. In addition to known clinical features of FH (raised total cholesterol or LDL-C and family history of premature coronary heart disease), machine-learning (ML) algorithms identified features such as raised triglycerides which reduced the likelihood of FH. Apart from logistic regression (AUC, 0.81), all four other ML approaches had similarly high predictive accuracy (AUC > 0.89). Calibration slope ranged from 0.997 for gradient boosting machines to 1.857 for logistic regression. Among those screened, high probability cases requiring clinical review varied from 0.73% using ensemble learning to 10.16% using deep learning, but with positive predictive values of 15.5% and 2.8% respectively. Ensemble learning exhibited a dominant positive likelihood ratio (45.5) compared to all other ML models (7.0-14.4). Machine-learning models show similar high accuracy in detecting FH, offering opportunities to increase diagnosis. However, the clinical case-finding workload required for yield of cases will differ substantially between models.