Smartphones increasingly serve as the source for, or to aggregate, a considerable amount of data that can be relevant in public health emergencies. Hence the sharing and utilisation of mobile health data, for example to help control the spread of communicable diseases, has become a relevant issue, with the COVID-19 pandemic adding a sudden urgency mirrored in debates around contact tracing apps. Building on exploratory work that indicated user perceptions and values around consent, and the notion that smartphones and mobile health data can be perceived as elements of self-embodiment, we present an online study comparing three scenarios of representative diseases undertaken during the first wave lockdown in the UK. Using a mixed-methods analysis of responses from 86 participants, we identify tensions and mitigations in user values and from those present the description of four characteristic user-groups that can inform considerations for design and development activities in this space.