Coe was born in Hammersmith, London. He grew up in Warwickshire and Sheffield. His mother, Tina Angela Coe, died in Hammersmith and Fulham, London, in 2005, aged 75. His mother was half Indian, born to a Punjabi father Sardari Lal and an English mother Vera. His father, Peter Coe (born Percy N. Coe in Kingston upon Thames), died on 9 August 2008, aged 88, while Coe was in Beijing.