Professor Balls studied zoology at Oxford University. He conducted research for a DPhil from Oxford at the University of Geneva Switzerland between 1961 and 1964. After post-doctoral research at the University of California, Berkeley, CA, and at Reed College, Portland, OR, from 1964 to 1966, he lectured in the School of Biological Sciences at the University of East Anglia. In 1975, he moved to the University of Nottingham Medical School as a senior lecturer in the Department of Human Morphology. Professor Balls became Reader in Medical Cell Biology in 1985 and was promoted to Professor of Medical Cell Biology in 1990. Since 1995, he has been an Emeritus Professor at Nottingham. He was a Trustee of Fund for the Replacement of Animals in Medical Experiments (FRAME) from 1979 until 2013, becoming editor of Alternatives to Laboratory Animals (ATLA) in 1983. Professor Balls was an adviser to the British government during the drafting and passage of the Animals (Scientific Procedures) Act 1986 and, from 1987–1995, was a founder member of the Animal Procedures Committee (which advises the Home Secretary on all matters related to animal experimentation). In 1993, he became the first Head of the European Centre for the Validation of Alternative Methods, retiring from this position in 2002.
Professor Balls has won a number of awards related to his work for animals in laboratories.