Health and social care (HSC) are marked by interwoven challenges of increasing need and demand, integrating digitization, and rights-based imperatives. Participatory governance may empower individuals and communities by involving them directly in decision-making processes and may be associated with better outcomes, but attitudes to it across Europe are unclear. We aimed to survey public attitudes around participatory governance. A cross-sectional, anonymous, online survey was administered to a European sample (N = 1198). The survey assessed attitudes to governance in HSC, with particular reference to a digital health platform. Demographic and psychosocial data were collected. Data were analyzed quantitatively. A majority endorsed health systems, governments, or the EU to own/operate/be trusted to manage data-sharing digital health platforms. There were positive dispositions to sharing data and patient or public participation in governance. Participants reported concerns about rights, ethical data use, and limited opportunities for governance participation. Age, education, rurality, income, activity limitation, digital confidence, technology acceptance, health literacy, and trust correlated with data sharing and governance. Differences between countries were evident. Women were more concerned about rights and ethical data use. Findings may assist in developing participatory models for governing digital networks in HSC. Such participation may advance inclusion in governing, decision-making, and oversight.