Born in Taunton, Somerset, Cecil Mary was motivated to study medicine by a spell in hospital in her teenage years. Graduating from Bristol University in 1942, she was then called up to serve in the Royal Army Medical Corps, where she attained the rank of captain. Despite requesting to serve overseas, she spent the war years on the home front, where while working at the War office she met Dr Barnet Woolf, a statistician and biochemist. They married in 1945 and moved to Edinburgh where their three children were born. Here she gained a national and international reputation for her work in paediatrics and her strong belief in publicly funded health care. In 1971 she accepted a consultancy and university appointment in Dundee.

She was one of a group of paediatricians who in the 1960s successfully challenged a practice that was stunting the lives of premature and low birthweight babies – ‘her prems’. In Edinburgh she carried out a study of 360 ‘prems’ born in the east of Scotland between 1953 and 1955; in 1964 she published The Growth and Development of the Prematurely Born Infant – a landmark study of a wide range of major factors affecting ‘prems.’ Her work in this and previous studies cast doubts on the prevailing orthodoxy, confirmed in major textbooks and in practice on both sides of the Atlantic, which delayed the first feeding of prematurely born babies for periods from 24 to 96 hours after birth. This had devastating effects on Scottish prems and her study prompted widespread changes in practice to start immediate feeding.
In Dundee Dr Drillien set up a new unit providing assessment and follow-up care for children with neurodevelopmental problems. She continued her research, showing the value of a closely-monitored pre-school developmental screening programme for children with special needs.

After her husband’s death in 1980 she lived in retirement in Edinburgh and North Berwick, where she took an Open University degree in history, and followed England’s fortunes in Test cricket.