Natural hair colour within European populations is a complex genetic trait. Previous work has established that MC1R variants are the principal genetic cause of red hair colour, but with variable penetrance. Here, we have extensively mapped the genes responsible for hair colour in the white, British ancestry, participants in UK Biobank. MC1R only explains 73% of the SNP heritability for red hair in UK Biobank, and in fact most individuals with two MC1R variants have blonde or light brown hair. We identify other genes contributing to red hair, the combined effect of which accounts for ~90% of the SNP heritability. Blonde hair is associated with over 200 genetic variants and we find a continuum from black through dark and light brown to blonde and account for 73% of the SNP heritability of blonde hair. Many of the associated genes are involved in hair growth or texture, emphasising the cellular connections between keratinocytes and melanocytes in the determination of hair colour.