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Physical activity and sleep duration are established risk factors for many diseases, but their aetiology is poorly understood, partly due to relying on self-reported evidence. Here we report a genome-wide association study (GWAS) of device-measured physical activity and sleep duration in 91,105 UK Biobank participants, finding 14 significant loci (7 novel). These loci account for 0.06% of activity and 0.39% of sleep duration variation. Genome-wide estimates of ~15% phenotypic variation indicate high polygenicity. Heritability is higher in women than men for overall activity (23 vs. 20%, p=1.5 x 10^-4) and sedentary behaviours (18 vs. 15%, p=9.7 x 10^-4). Heritability partitioning, enrichment and pathway analyses indicate the central nervous system plays a role in activity behaviours. Two-sample Mendelian randomisation suggests that increased activity might causally lower diastolic blood pressure (beta mmHg/SD: -0.91, SE=0.18, p=8.2 x 10^-7), and odds of hypertension (Odds ratio/SD: 0.84, SE=0.03, p=4.9 x 10^-8). Our results advocate the value of physical activity for reducing blood pressure.