Ogdon was born in Mansfield Woodhouse, Nottinghamshire, and attended the Manchester Grammar School, before studying at the Royal Northern College of Music (formerly The Royal Manchester College of Music) between 1953 and 1957, where his fellow students under Richard Hall included Harrison Birtwistle, Alexander Goehr, Elgar Howarth and Peter Maxwell Davies. Together they formed New Music Manchester, a group dedicated to the performances of serial and other modern works. His tutor there was Claud Biggs. As a boy he had studied with Iso Elinson and after leaving college, he further studied with Gordon Green, Denis Matthews, Dame Myra Hess, and Egon Petri—the last in Basel, Switzerland.