Alongside efforts to improve evidence use in policy, grassroots demands and governance-driven democratisation are informing an ever-increasing range of public engagement processes in UK policy. This article explores how these simultaneous efforts intersect within three policy organisations working at different levels of UK policy: local (Sheffield City Council), regional (Greater Manchester Combined Authority) and national (devolved) (Scottish Government). Employing documentary analysis and 51 interviews with individuals working in these organisations, we argue that there are organisational similarities in approaches to evidence and engagement, including: conceiving of both ‘data’ (statistics tracked by internal analysts) and ‘evidence’ (external analysis) in primarily quantified terms; and a tendency to limit the authority of publics to advising and consulting on predefined issues. Yet, we also find growing interest in more in-depth understandings of publics (for example, via ‘lived experiences’) but uncertainty about how to use these qualitative insights in settings that have institutionalised quantitative approaches to evidence. We identify four distinct responses: (1) prioritising public engagement; (2) strategically using public engagement and evidence to support policy proposals; (3) prioritising quantified evidence and data; and (4) attempting to integrate these distinct knowledge types. Surprisingly (given the organisational importance afforded to metrics), we categorised most interviewees in Cluster 4. Finally, we explore how interviewees described trying to do this kind of integration work, before reflecting on the promise and limitations of the various mechanisms that interviewees identified.