UK Biobank (UKB) is a key contributor in mental health genome-wide association studies (GWAS) but only ~31% of participants completed the Mental Health Questionnaire (MHQ responders). We predicted generalized anxiety disorder (GAD), posttraumatic stress disorder (PTSD), and major depression symptoms using elastic net regression in the ~69% of UKB participants lacking MHQ data (MHQ non-responders; NTraining=50%; NTest=50%), maximizing the informative sample for these traits. MHQ responders were more likely to be female, from higher socioeconomic positions, and less anxious than non-responders. Genetic correlation of GAD and PTSD between MHQ responders and non-responders ranged from 0.636-1.08; both were predicted by polygenic scores generated from independent cohorts. In meta-analyses of GAD (N=489,579) and PTSD (N=497,803), we discovered many novel genomic risk loci (13 for GAD and 40 for PTSD). Transcriptomic analyses converged on altered regulation of prenatal dorsolateral prefrontal cortex in these disorders.