With the use of genetic technology, researchers have the potential to inform medical diagnoses and treatment in actionable ways. Accurate variant interpretation is a necessary condition for the utility of genetic technology to unfold. This relies on the ability to access large genomic datasets so that comparisons can be made between variants of interest. This can only be successful if DNA and medical data are donated by large numbers of people to ‘research’, including clinical, non-profit and for-profit research initiatives, in order to be accessed by scientists and clinicians worldwide. The objective of the ‘Your DNA, Your Say’ global survey is to explore public attitudes, values and opinions towards willingness to donate and concerns regarding the donation of one's personal data for use by others. Using a representative sample of 8967 English-speaking publics from the UK, the USA, Canada and Australia, we explore the characteristics of people who are unwilling (n = 1426) to donate their DNA and medical information, together with an exploration of their reasons. Understanding this perspective is important for making sense of the interaction between science and society. It also helps to focus engagement initiatives on the issues of concern to some publics.