People having access to their medical records could have a transformative improvement effect on healthcare delivery and use. Our research aimed to explore the concerns and attitudes of giving people electronic access to their medical records through patient portals. We conducted 28 semi-structured interviews with 30 people, asking questions about portal design, organisational implications and governance. We report the findings of the governance considerations raised during the interviews. These revealed that (1) there is uncertainty about the possible design and extent of giving people access to their medical records to view/use, (2) existing policies about patient authentication, proxy, and privacy require modification, and (3) existing governance structures and functions require further examination and adjustment. Future research should include more input from patients and health informaticians.