In recent years, researchers have begun to explore the use of Distributed Ledger Technologies (DLT), also known as blockchain, in health data sharing contexts. However, there is a significant lack of research that examines public attitudes towards the use of this technology. In this paper, we begin to address this issue and present results from a series of focus groups which explored public views and concerns about engaging with new models of personal health data sharing in the UK. We found that participants were broadly in favour of a shift towards new decentralised models of data sharing. Retaining ‘proof’ of health information stored about patients and the capacity to provide permanent audit trails, enabled by immutable and transparent properties of DLT, were regarded as particularly valuable for our participants and prospective data custodians. Participants also identified other potential benefits such as supporting people to become more health data literate and enabling patients to make informed decisions about how their data was shared and with whom. However, participants also voiced concerns about the potential to further exacerbate existing health and digital inequalities. Participants were also apprehensive about the removal of intermediaries in the design of personal health informatics systems.