Genetically informed and deep-phenotyped biobanks are an important research resource. The cost of phenotyping far outstrips that of genotyping, and therefore it is imperative that the most powerful, versatile and efficient analysis approaches are used. Here, we apply our recently developed Bayesian grouped mixture of regressions model (GMRM) in the UK and Estonian Biobanks and obtain the highest genomic prediction accuracy reported to date across 21 heritable traits. On average, GMRM accuracies were 15% (SE 7%) greater than prediction models run in the LDAK software with SNP annotation marker groups, 18% (SE 3%) greater than a baseline BayesR model without SNP markers grouped into MAF-LD-annotation categories, and 106% (SE 9%) greater than polygenic risk scores calculated from mixed-linear model association (MLMA) estimates. For height, the prediction accuracy R 2 was 47% in a UK Biobank hold-out sample, which was 76% of the estimated . We then extend our GMRM prediction model to provide MLMA SNP marker estimates for GWAS discovery, which increased the independent loci detected to 7,910 in unrelated UK Biobank individuals, as compared to 5,521 from BoltLMM and 5,727 from Regenie, a 43% and 38% increase respectively. The average χ 2 value of the leading markers was 34% (SE 5.11) higher for GMRM as compared to Regenie, and increased by 17% for every 1% increase in prediction accuracy gained over a baseline BayesR model across the traits. Thus, we show that modelling genetic associations accounting for MAF and LD differences among SNP markers, and incorporating prior knowledge of genomic function, is important for both genomic prediction and for discovery in large-scale individual-level biobank-scale studies.