Tozer studied with Eileen Ralf and Keith Humble in Australia, Maria Curcio (the last and favourite pupil of Artur Schnabel) in England and Theodore Lettvin in the United States. Eileen Ralf lived in Hobart, and the airline TAA flew Tozer there and back every week for lessons, free of charge. He later described Ralf's teaching as "the greatest musical gift given me". Aged 14, he became the youngest semi-finalist ever at the Leeds International Piano Competition and soon afterwards made his European debut at a BBC Promenade Concert in the Royal Albert Hall, with the BBC Symphony Orchestra under Sir Colin Davis. He was the youngest person to be awarded a Churchill Fellowship.