Box was born at Fulham and studied at Cornwall College. Working for a period at the Celtic Pottery in Newlyn, Ian travelled overland around the world to India, Australia, and back to Cornwall. He attended Redruth Art School in 1971, and was offered a place at the Leach Pottery by Janet LEACH after she had viewed his diploma show in 1974. That secondment allowed him to gain the Licentiate of the Society of Industrial Arts and Designers in 1975.
Ian began his own stoneware pottery business in Penzance in 1976, and on selling it in 1982 he worked as a technician at Falmouth College of Art. From 1984 he taught ceramics and social education at the John Daniel Centre for people with learning difficulties. The Newlyn Art Gallery hosted a show of the students' work in 1999, which was brilliantly reviewed and well attended, virtually everything being sold.