Objective The relationship between insomnia symptoms and cognitive performance is unclear, particularly at the population level. We conducted the largest examination of this association to date through analysis of the UK Biobank, a large population-based sample of adults aged 40–69 years. We also sought to determine associations between cognitive performance and self-reported chronotype, sleep medication use and sleep duration. Methods This cross-sectional, population-based study involved 477,529 participants, comprising 133,314 patients with frequent insomnia symptoms (age: 57.4 ± 7.7 years; 62.1% female) and 344,215 controls without insomnia symptoms (age: 56.1 ± 8.2 years; 52.0% female). Cognitive performance was assessed by a touchscreen test battery probing reasoning, basic reaction time, numeric memory, visual memory, and prospective memory. Adjusted models included relevant demographic, clinical, and sleep variables. Results Frequent insomnia symptoms were associated with cognitive impairment in unadjusted models; however, these effects were reversed after full adjustment, leaving those with frequent insomnia symptoms showing statistically better cognitive performance over those without. Relative to intermediate chronotype, evening chronotype was associated with superior task performance, while morning chronotype was associated with the poorest performance. Sleep medication use and both long (>9 h) and short (<7 h) sleep durations were associated with impaired performance. Conclusions Our results suggest that after adjustment for potential confounding variables, frequent insomnia symptoms may be associated with a small statistical advantage, which is unlikely to be clinically meaningful, on simple neurocognitive tasks. Further work is required to examine the mechanistic underpinnings of an apparent evening chronotype advantage in cognitive performance and the impairment associated with morning chronotype, sleep medication use, and sleep duration extremes.