Johnson was born in Chapelton, a small town in the rural parish of Clarendon, Jamaica. His middle name, "Kwesi", is a Ghanaian name that is given to boys who, like Johnson, are born on a Sunday. In 1963 he and his father came to live in Brixton, London, joining his mother, who had immigrated to Britain shortly before Jamaican independence in 1962. Johnson attended Tulse Hill School in Lambeth. While still at school he joined the British Black Panther Movement, helped to organise a poetry workshop within the movement, and developed his work with Rasta Love, a group of poets and drummers.