Participant motion in brain magnetic resonance imaging is associated with processing problems including potentially non-useable/incomplete data. This has implications for representativeness in research. Few large studies have investigated predictors of increased motion in the first instance. We exploratively tested for association between multiple psychological and physical health traits with concurrent motion during T1 structural, diffusion, average resting-state and task functional magnetic resonance imaging in N = 52 951 UK Biobank imaging subsample participants. These traits included history of cardiometabolic, inflammatory, neurological and psychiatric conditions, as well as concurrent cognitive test scores and anthropometric traits. We tested for stability in motion in participants with longitudinal imaging data (n = 5305, average 2.64 years later). All functional and T1 structural motion variables were significantly intercorrelated (Pearson r range 0.3-0.8, all P < 0.001). Diffusion motion variables showed weaker correlations around r = 0.1. Most physical and psychological phenotypes showed significant association with at least one measure of increased motion including specifically in participants with complete useable data (highest β = 0.66 for diabetes versus resting-state functional magnetic resonance imaging motion). Poorer values in most health traits predicted lower odds of complete imaging data, with the largest association for history of traumatic brain injury (odds ratio = 0.720, 95% confidence interval = 0.562 to 0.923, P = 0.009). Worse psychological and physical health are consistent predictors of increased average functional and structural motion during brain imaging and associated with lower odds of complete data. Average motion levels were largely consistent across modalities and longitudinally in participants with repeat data. Together, these findings have implications for representativeness and bias in imaging studies of generally healthy population samples.