Cossey was born in Brooke, Norfolk. Through puberty, Cossey was distinctly feminine in appearance due to a variant of Klinefelter's syndrome, where, instead of having the XY chromosome pattern, she possesses the genotype XXXY (people with Klinefelter's syndrome usually have XXY). In Cossey's autobiography My Story, she describes an unhappy childhood, where she suffered confusing feelings and bullying by peers due to her femininity. Growing up, Cossey's closest companion was her sister, Pam, with whom she played dress up in their mother's clothes. Cossey left formal schooling when she was fifteen, and found work in a clothing store and as a butcher's apprentice. At sixteen she moved to London and worked at a variety of low-wage jobs.