 Keen was born in 1925 in London to a Jewish family; his parents were Sydney Keen, a tailor, and Esther (née Zenober), a teacher who had migrated to the United Kingdom from Poland.He attended St Ann's School in Hanwell and Ealing County Grammar School for Boys.He studied medicine at St Mary's Hospital Medical School, graduating on 5 July 1948, the day that the National Health Service (NHS) was established.