Automated online and App-based cognitive assessment tasks are becoming increasingly popular in large-scale cohorts and biobanks due to advantages in affordability, scalability, and repeatability. However, the summary scores that such tasks generate typically conflate the cognitive processes that are the intended focus of assessment with basic visuo-motor speeds, testing device latencies, and speed-accuracy tradeoffs. This lack of precision presents a fundamental limitation when studying brain-behaviour associations. Previously, we developed a novel modelling approach that leverages continuous performance recordings from large-cohort studies to achieve an iterative decomposition of cognitive tasks (IDoCT), which outputs data-driven estimates of cognitive abilities, and device and visuo-motor latencies, whilst recalibrating trial-difficulty scales. Here, we further validate the IDoCT approach with UK BioBank imaging data. First, we examine whether IDoCT can improve ability distributions and trial-difficulty scales from an adaptive picture-vocabulary task (PVT). Then, we confirm that the resultant visuo-motor and cognitive estimates associate more robustly with age and education than the original PVT scores. Finally, we conduct a multimodal brain-wide association study with free-text analysis to test whether the brain regions that predict the IDoCT estimates have the expected differential relationships with visuo-motor versus language and memory labels within the broader imaging literature. Our results support the view that the rich performance timecourses recorded during computerised cognitive assessments can be leveraged with modelling frameworks like IDoCT to provide estimates of human cognitive abilities that have superior distributions, re-test reliabilities, and brain-wide associations.