She was educated at Southend High School for Girls, a grammar school in Southend-on-Sea. She studied at University College London, from which she gained a Bachelor of Science (BSc) degree in botany and a Doctor of Philosophy (PhD) degree in 1964.
Casselton was born on 18 July 1938 in Rochford, Essex to William Charles Henry Smith and Cecile Smith (née Bowman). Her parents' smallholding and her father's interest in natural history and genetics encouraged her and her sister Pauline in the direction of biology.