Born in Cardiff, Box was educated at The Cathedral School, Llandaff, St John's School in Pinner, and Harrow County School for Boys. He joined the stockbrokers' company Henry J. Thomas at the age of 17.
Box, who was born in Cardiff, attended several schools including The Cathedral School, Llandaff, St John's School in Pinner, and Harrow County School for Boys before joining the investment company Henry J. Thomas at the age of 17.