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, pursued his academic career at several institutions including The Cathedral School, Llandaff, St John's School in Pinner, and Harrow County School for Boys before securing a position at the financial services firm Henry J. Thomas at the age of 17.