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Baines was born on 17 March 1946. He is the oldest son of Edward Russell Baines and his wife Dora Margaret Jean (née O’Brien). He was educated at Winchester College, an all boys public boarding school in Winchester, Hampshire, England. He went on to study Egyptology at the University of Oxford. He graduated with a Bachelor of Arts degree (BA) in 1967, later promoted to Master of Arts (MA). He gained his Doctor of Philosophy degree (DPhil) in 1976.