A number of Graham's friends had been to Jamaica in the previous ten years, and were glowing in their reviews of the newly independent nation. Many encouraged him to visit. Soon an invitation came from Henry Fowler, the founder of the Priory School, for him to go and head the art department there for a year. Graham accepted, and thus began the Jamaican chapter of his life.

His initial years at Priory were a resounding success. The cultural transition was smooth, as, at the time, there was an almost seamless union between the significant expatriate presence and the local intellectual and artistic community in the country. His contract was renewed at the end of the first year for three more years. A sabbatical for three and then six months meant that Graham could travel extensively, which he did, touring Latin America and the Caribbean. He became involved in local theatre productions, rented a hut in the hills of Kingston where he lived modestly, and started selling his paintings. He felt that it was an idyllic existence.

The second half of the seventies was more tumultuous. Now in his early thirties, he was becoming more concerned about his economic future, as was his family back in England. This was, for him, a period of academic activity abroad, teaching at the Miami Museum of Art, having exhibitions in London, visiting Russia with a group of artists, all the time being implored to return to the UK to take over part of the family business.

The death of Graham's father in 1977 precipitated his decision to leave Jamaica for good to be with his stepmother in England. Perhaps his most nomadic yet productive period in the seventies saw more exhibitions in the UK and America. The event of his stepmother's remarriage coupled with the death of a good friend in Jamaica resulted in an unplanned return to the Caribbean. He contemplated a move to Greece with his widowed friend, and even spent a few months there attempting to learn the language, only to return to Jamaica in 1979 to live in a hut in Ocho Rios with his friend, by the sea.