Government at all levels in the UK and around the world face increasing challenges in regulating and governing their own use of data and data technologies, including at the local level. At the same time publics are increasingly aware of and critical towards incidents of data misuse and unethical data technology development. One solution to addressing these socio-technical questions of good government data use is public debate and inclusion through public engagement. In order to empirically develop a base on which such public engagement could rest, our aim is to compare and contrast different views on public engagement on government data use in the UK. We conducted a series of seven focus groups with government, technical, and nontechnical publics on this topic. Transcripts from these focus groups were thematically analysed by group for common themes. All three groups expressed wariness towards increased data collection and monitoring, as well as a sense of criticism on whether local governments use data effectively in policy decision-making. In discussing their views of public engagement, the technical and government groups expressed concerns on the 'public' being data illiterate and all three groups imagined the 'public' as disinterested in data use and policy-making. In contrast, good public engagement was described as focusing both on the means and ends of policy-making with data, being influential on local government process, and offering multiple mechanisms of participation. In conclusion, while good public engagement is imagined as empowering and beneficial to publics and data technology development alike, participants struggled to imagine a public that would be interested in public engagement exercises. is suggests a first step in developing public engagement exercises on government data use within the UK is reflecting on the mechanisms that may lead to an actual or assumed disinterested and unaware public.