He is of mixed heritage. His father is English, with Scottish ancestry. His mother was born in Singapore but is of Indian Tamil ethnicity. In the 1950s when she was in her teens her family drove from Tamil Nadu, India to London, United Kingdom. Their journey is documented in The Times archive. His father (Peter), was a civil servant, working as a probation officer in tough areas such as Tottenham and Holloway. His mother (Leela) taught English to refugees and also literacy to Category A prisoners at HM Prison Wormwood Scrubs. She also worked as a music teacher. Floyd has two older brothers, one of whom is Sky Sports broadcaster Matt Kabir.
