When it comes to using patient data from the National Health Service (NHS) for research, we are often told that it is a matter of trust: we need to trust, we need to build trust, we need to restore trust. Various policy papers and reports articulate and develop these ideas and make very important contributions to public dialogue on the trustworthiness of our research institutions. But these documents and policies are apparently constructed with little sustained reflection on the nature of trust and trustworthiness, and therefore are missing important features that matter for how we manage concerns related to trust. We suggest that what we mean by ‘trust’ and ‘trustworthiness’ matters and should affect the policies and guidance that govern data sharing in the NHS. We offer a number of initial, general reflections on the way in which some of these features might affect our approach to principles, policies and strategies that are related to sharing patient data for research. This paper is the outcome of a ‘public ethics’ coproduction activity which involved members of the public and two academic ethicists. Our task was to consider collectively the accounts of trust developed by philosophers as they applied in the context of the NHS and to coproduce an argumentative position relevant to this context.