Miller was educated at Taunton School and St Paul's School, London where he developed an early (and ultimately lifelong) interest in the biological sciences. While at St Paul's School at the age of 12, Miller met and became close friends with Oliver Sacks and Sacks's best friend Eric Korn, friendships which remained crucial throughout the rest of their lives. In 1953, before leaving secondary school, he performed comedy several times on the BBC radio program "Under Twenty Parade". Miller studied natural sciences and medicine at St John's College, Cambridge (MB BChir, 1959), where he was a member of the Cambridge Apostles before going on to train at University College Hospital in London.