The genetic structure in Europe was mostly shaped by admixture between the Western Hunter-Gatherers, Early European Farmers and Steppe Bronze Age ancestral components. Such structure is regarded as a confounder in GWAS and follow-up studies, and gold-standard methods exist to correct for it. However, it is still poorly understood to which extent these ancestral components contribute to complex trait variation in present-day Europe. In this work we harness the UK Biobank to address this question. By extensive demographic simulations, exploiting data on siblings and incorporating previous results we obtained from the Estonian Biobank, we carefully evaluate the significance and scope of our findings. Heart rate, platelet count, bone mineral density and many other traits show stratification similar to height and pigmentation traits, likely targets of selection and divergence across ancestral groups. We show that the reported ancestry-trait associations are not driven by environmental confounders by confirming our results when using between-sibling differences in ancestry. The consistency of our results across biobanks further supports this and indicates that these genetic predispositions that derive from post-Neolithic admixture events act as a source of variability and as potential confounders in Europe as a whole.