Miller grew up in St John's Wood, London, in a well-connected Jewish family. His father Emanuel (1892–1970), who was of Lithuanian descent and suffered from severe rheumatoid arthritis, was a military psychiatrist and subsequently a paediatric psychiatrist at Harley House. His mother, Betty Miller (née Spiro) (1910–1965), was a novelist and biographer who was originally from County Cork, Ireland. Miller had an elder sister, Sarah (died 2006) who worked in television for many years and retained an involvement with Judaism that Miller, as an atheist, always eschewed. As a child Miller had a stammer and was attention-seeking, compensating for his stammer by speaking in foreign accents. He also developed an astonishing talent for mimicry, including chickens and steamtrains. The young Miller was assessed by several child psychiatrists, including Donald Winnicott. He had many sessions, as a teenager with the psychiatrist Leopold Stein. Miller enjoyed the sessions and said that they "simply conversed about philosophy and Hughlings Jackson's early neurological theories".
Miller moved between several different schools prior to attending Taunton School, including for a time at the Rudolf Steiner School Kings Langley (a Waldorf school) where he was taught by two of Ivy Compton-Burnett's sisters and says of that time that he "never learnt anything at all". Miller concluded his secondary school education at 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 programme 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 and one of cast’s three Granta cartoonist, before going on to train at University College Hospital in London.
While studying medicine, Miller was involved in the Cambridge Footlights, appearing in the revues Out of the Blue (1954) and Between the Lines (1955). Good reviews for these shows, and for Miller's performances in particular, led to his performing on a number of radio and television shows while continuing his studies; these included appearances on Saturday Night on the Light, Tonight and Sunday Night at the London Palladium. He qualified as a physician in 1959 and then worked as a hospital house officer for two years, including at the Central Middlesex Hospital as house physician for gastroenterologist Francis Avery Jones.
