Hammersmith, London. His father was athletics coach Peter Coe and his mother, Tina Angela Lal, was of half Indian descent, born to a Punjabi father, Sardari Lal Malhotra, and an English/Irish mother, Vera (née Swan). Indian diplomat Samar Sen was Sebastian's uncle.

When he was less than a year old, Coe and his family moved to Warwickshire,