Born to political active family, both of her parents are Socialists. Her father works as an architect and teacher, while her mother Susie is a teacher, supporting the feminist movement. In childhood, she sold the Socialist Worker newsletter for pocket money, attended marches and rallies after school with her activist mother and stepfather and even shared her home with striking miners.
She was discovered at 15 in Covent Garden, by the same scout who discovered Naomi Campbell, and embarked on a successful career as a model. She modeled in Paris and London for Chanel, Yves Saint-Laurent and Vivienne Westwood. But she'd studied drama since she was a child and made her first film at the age of 17, leaving the catwalk behind.
2006 UK newspaper "The Independent"'s Pink List - a list of the most influential gay men and women - placed Burrows at no. 90, citing a rumored relationship with "Harry Potter" and The Black Dahlia (2006) actress Fiona Shaw.