Born in Accrington, Lancashire, England, on 9 March 1941, Halton was the only child of John Henry Halton and Mary (May) Halton (née Robinson). He contracted bovine tuberculosis as a young child and consequently missed two years of his early education. Later he attended St Josephs College, Blackpool, and St Josephs Academy, Blackheath. After winning a state scholarship, Halton studied chemistry at the University of Southampton, graduating BSc(Hons) in 1963. He went on to complete a PhD supervised by Richard Cookson at the same institution in 1966. His two-part thesis was titled Part I: Addition reactions of a methyleneaziridine. Part II: Conformational aspects of cyclotriveratrylene derivatives.
Halton moved to Wellington, New Zealand, in 1968, and married Margaret Leach in 1970. The couple went on to have two children. In 1980, Halton became a naturalised New Zealander.