Kebbell, the fourth of five children, was born in Pontefract, Yorkshire, but grew up in Nottinghamshire where he attended The Grove School (now the Newark Academy) in Balderton. He was brought up by his mother, Michelle (née Mathers), a cook and landscape gardener and his father, Robert Kebbell, an engineer from Zimbabwe. He was raised Catholic and attended a Catholic primary school.
Kebbell trained in acting at the Central Junior Television Workshop in Nottingham along with Andrew Shim and Vicky McClure.